Download Stat 201 Quiz 4

Click Link below To Purchase:
http://www.madehomework.com/product-category/stat-201/
Stat 201 Quiz 4
1 A local trucking company fitted a regression to relate the travel time (days) of its
shipments as a function of the distance traveled (miles). The fitted regression is
Time = -7.126 + 0.0214 Distance, based on a sample of 20 shipments. The
estimated standard error of the slope is 0.0053. Find the value of tcalc to test for
zero slope.
2.46
5.02
4.04
3.15
2 If the attendance at a baseball game is to be predicted by the equation Attendance
= 16,500 – 75 Temperature, what would be the predicted attendance if
Temperature is 90 degrees?
6,750
9,750
12,250
10, 020
3 A researcher’s results are shown below using Femlab (labor force participation
rate among females) to try to predict Cancer (death rate per 100,000 population
due to cancer) in the 50 U.S. states.
What is the R2 for this regression?
.9018
.0982
.8395
.1605
4 Mary used a sample of 68 large U.S. cities to estimate the relationship between
Crime (annual property crimes per 100,000 persons) and Income (median annual
income per capita, in dollars). Her estimated regression equation was Crime = 428
+ 0.050 Income. If Income decreases by 1000, we would expect that Crime will:
increase by 428.
decrease by 50.
increase by 500.
remain unchanged.
5 Amelia used a random sample of 100 accounts receivable to estimate the
relationship between Days (number of days from billing to receipt of payment) and
Size (size of balance due in dollars). Her estimated regression equation was Days =
22 + 0.0047 Size with a correlation coefficient of .300. From this information we
can conclude that:
9 percent of the variation in Days is explained by Size.
autocorrelation is likely to be a problem.
the relationship between Days and Size is significant.
larger accounts usually take less time to pay.
6 Simple regression analysis means that:
the data are presented in a simple and clear way.
we have only a few observations.
there are only two independent variables.
we have only one explanatory variable.
7 Which is not true of the coefficient of determination?
It is the square of the coefficient of correlation.
It is negative when there is an inverse relationship between X and Y.
It reports the percent of the variation in Y explained by X.
It is calculated using sums of squares (e.g., SSR, SSE, SST).
8 If the fitted regression is Y = 3.5 + 2.1X (R2 = .25, n = 25), it is incorrect to
conclude that:
Y increases 2.1 percent for a 1 percent increase in X.
the estimated regression line crosses the Y axis at 3.5.
the sample correlation coefficient must be positive.
the value of the sample correlation coefficient is 0.50.
9 Which is correct to find the value of the coefficient of determination (R2)?
SSR/SSE
SSR/SST
1 – SST/SSE
10 The critical value for a two-tailed test of H0: β1 = 0 at α = .05 in a simple
regression with 22 observations is:
±1.725
±2.086
±2.528
±1.960
Stat 201 Homework 2 Chapter 6
1 A lottery ticket has a grand prize of $34 million. The probability of winning the
grand prize is .000000025.
Determine the expected value of the lottery ticket. (Round your answer to 3
decimal places.)
Would you pay $1 for a ticket?
Write the probability of each italicized event in symbols (e.g., P(X ≥ 5).
(a) At least 5 correct answers on a 20-question quiz (X = number of correct
answers).
P(X ≥ 5)
P(X < 5) P(X ≤ 5) P(X > 5)
(b) Fewer than 8 “phishing” e-mails out of 30 e-mails (X = number of phishing emails).
P(X > 8)
P(X ≤ 8)
P(X < 8)
P(X ≥ 8)
(c) At most 8 no-shows at a party where 24 guests were invited (X = number of noshows).
P(X ≥ 8)
P(X < 8) P(X > 8)
P(X ≤ 8)
5 Calculate each binomial probability:
(a) X = 2, n = 8, π = 0.20 (Round your answer to 4 decimal places.)
(b) X = 2, n = 5, π = 0.50 (Round your answer to 4 decimal places.)
(c) X = 1, n = 10, π = 0.15 (Round your answer to 4 decimal places.)
6 Calculate each binomial probability:
Fewer than 4 successes in 15 trials with a 15 percent chance of success. (Round
your answer to 4 decimal places.)
At least 4 successes in 8 trials with a 30 percent chance of success. (Round your
answer to 4 decimal places.)
At most 8 successes in 17 trials with a 60 percent chance of success. (Round your
answer to 4 decimal places.)
Historically, 7 percent of a mail-order firm’s repeat charge-account customers have
an incorrect current address in the firm’s computer database.
The number of customers out of 14 who have an incorrect address in the database
is a binomial random variable with n = 14 and π = 0.07.
What is the probability that none of the next 14 repeat customers who call will
have an incorrect address? (Round your answer to 4 decimal places.)
What is the probability that three customer who call will have an incorrect address?
(Round your answer to 4 decimal places.)
What is the probability that four customers who call will have an incorrect
address? (Round your answer to 4 decimal places.)
What is the probability that fewer than five customers who call will have an
incorrect address? (Round your answer to 4 decimal places.)
11 Police records in the town of Saratoga show that 11 percent of the drivers
stopped for speeding have invalid licenses. If 22 drivers are stopped for speeding,
find the probabilities.
None will have an invalid license. (Round your answer to 4 decimal places.)
Exactly three will have an invalid license. (Round your answer to 4 decimal
places.)
At least 4 will have invalid licenses. (Round your answer to 4 decimal places.)
12 Calculate each Poisson probability:
P(X = 4), λ = 0.30 (Round your answer to 7 decimal places.)
P(X = 3), λ = 4.20 (Round your answer to 4 decimal places.)
P(X = 5), λ = 3.60 (Round your answer to 4 decimal places.)
13 Calculate each Poisson probability:
Fewer than 5 arrivals with λ = 5.90. (Round your answer to 5 decimal places.)
At least 4 arrivals with λ = 4.90. (Round your answer to 5 decimal places.)
At most 10 arrivals with λ = 8.00. (Round your answer to 5 decimal places.)
14 As a birthday gift, you are mailing a new personal digital assistant (PDA) to
your cousin in Toledo. The PDA cost $446. There is a 4 percent chance it will be
lost or damaged in the mail. Is it worth $4 to insure the mailing?
15 The probability that an American CEO can transact business in a foreign
language is .30. Eleven American CEOs are chosen at random.
What is the probability that none can transact business in a foreign language?
(Round your answer to 4 decimal places.)
What is the probability that at least two can transact business in a foreign
language? (Round your answer to 4 decimal places.)
What is the probability that all 11 can transact business in a foreign language?
(Round your answer to 10 decimal places.)
14 As a birthday gift, you are mailing a new personal digital assistant (PDA) to
your cousin in Toledo. The PDA cost $446. There is a 4 percent chance it will be
lost or damaged in the mail. Is it worth $4 to insure the mailing?
15 The probability that an American CEO can transact business in a foreign
language is .30. Eleven American CEOs are chosen at random.
What is the probability that none can transact business in a foreign language?
(Round your answer to 4 decimal places.)
What is the probability that at least two can transact business in a foreign
language? (Round your answer to 4 decimal places.)
What is the probability that all 11 can transact business in a foreign language?
(Round your answer to 10 decimal places.)
On average, 50 percent of U.S. beer drinkers order light beer.
What is the probability that none of the next eight customers who order beer will
order light beer? (Round your answer to 4 decimal places.)
What is the probability that one of the next eight customers who order beer will
order light beer? (Round your answer to 4 decimal places.)
What is the probability that two of the next eight customers who order beer will
order light beer? (Round your answer to 4 decimal places.)
What is the probability that fewer than three of the next eight customers who order
beer will order light beer? (Round your answer to 4 decimal places.)
17 Car security alarms go off at a mean rate of 3.3 per hour in a large Costco
parking lot.
Find the probability that in an hour there will be (Round your answers to 4 decimal
places.)
18 Past insurance company audits have found that 3 percent of dependents claimed
on an employee’s health insurance actually are ineligible for health benefits. An
auditor examines a random sample of 7 claimed dependents.
What is the probability that all are eligible? (Round your answer to 4 decimal
places.)
What is the probability that at least one is ineligible? (Round your answer to 4
decimal places.)
19 In Northern Yellowstone Lake, earthquakes occur at a mean rate of 1.2 quakes
per year. Let X be the number of quakes in a given year.
Justify the use of the Poisson model.
What is the probability of fewer than three quakes? (Round your answer to 4
decimal places.)
What is the probability of more than five quakes? (Round your answer to 4
decimal places.)
Stat 201 Homework 3 Chapter 7
1 A continuous uniform distribution U(0,800) will have μ = 400 and σ = 230.94.
True
False
2 A continuous uniform distribution U(100,200) will have the same standard
deviation as a continuous uniform distribution U(200,300).
True
False
3 The exponential distribution describes the number of arrivals per unit of time.
True
False
4 If arrivals follow a Poisson distribution, waiting times follow the exponential
distribution.
True
False
5 For a continuous random variable, the total area beneath the PDF will be greater
than zero but less than one.
True
False
6 A random variable X is best described by a continuous uniform distribution from
20 to 45 inclusive. The mean of this distribution is:
30.5.
31.5.
32.5.
33.5.
7 If arrivals occur at a mean rate of 3.6 events per hour, the exponential probability
of waiting less than 0.5 hour for the next arrival is:
.7122.
.8105.
.8347.
.7809.
8 Bob’s z-score for the last exam was 1.52 in Prof. Axolotl’s class BIO 417, “Life
Cycle of the Ornithorhynchus.” Bob said, “Oh, good, my score is in the top 10
percent.” Assuming a normal distribution of scores, is Bob right?
Yes.
No.
Must have n to answer.
9 The lengths of brook trout caught in a certain Colorado stream are normally
distributed with a mean of 14 inches and a standard deviation of 3 inches. The first
quartile for the lengths of brook trout would be:
16.01 inches.
11.00 inches.
11.98 inches.
10.65 inches.
10 The lengths of brook trout caught in a certain Colorado stream are normally
distributed with a mean of 14 inches and a standard deviation of 3 inches. What
lower limit should the State Game Commission set on length if it is desired that 80
percent of the catch may be kept by fishers?
12.80 inches
11.48 inches
12.00 inches
9.22 inches
11 Chlorine concentration in a municipal water supply is a uniformly distributed
random variable that ranges between 0.61 ppm and 0.95 ppm.
What is the mean chlorine concentration? (Round your answer to 2 decimal
places.)
Calculate the standard deviation? (Round your answer to 4 decimal places.)
What is the probability that the chlorine concentration will exceed 0.75 ppm on a
given day? (Round your answer to 4 decimal places.)
What is the probability that the chlorine concentration will be under 0.63 ppm?
(Round your answer to 4 decimal places.)
What is the probability that the chlorine concentration will be between 0.80 ppm
and 0.94 ppm? (Round your answer to 4 decimal places.)
12
The fracture strength of a certain type of manufactured glass is normally
distributed with a mean of 503 MPa with a standard deviation of 13 MPa.
(a) What is the probability that a randomly chosen sample of glass will break at
less than 503 MPa? (Round your answer to 2 decimal places.)
What is the probability that a randomly chosen sample of glass will break at more
than 519 Mpa? (Round your answer to 4 decimal places.)
What is the probability that a randomly chosen sample of glass will break at less
than 528 MPa? (Round your answer to 4 decimal places.)
13 If the weight (in grams) of cereal in a box of Lucky Charms is N(470,5), what is
the probability that the box will contain less than the advertised weight of 453 gm?
Note: You may need to use Excel to calculate the exact probabilities. (Round your
answer to 5 decimal places.)
14 The amount of fill in a half-liter (500 ml) soft drink bottle is normally
distributed. The process has a standard deviation of 2.0 ml. The mean is adjustable.
Where should the mean be set to ensure a 90 percent probability that a half-liter
bottle will not be underfilled? (Round your answer to 2 decimal places.)
Where should the mean be set to ensure a 95 percent probability that a half-liter
bottle will not be underfilled? (Round your answer to 2 decimal places.)
Where should the mean be set to ensure a 99.0 percent probability that a half-liter
bottle will not be underfilled? (Round your answer to 2 decimal places.)
15
Automobile warranty claims for engine mount failure in a Troppo Malo 2000 SE
are rare at a certain dealership, occurring at a mean rate of 0.11 claim per month.
(a) What is the probability that the dealership will wait at least 4 months until the
next claim? (Round your answer to 4 decimal places.)
What is the probability that the dealership will wait at least a year? (Round your
answer to 4 decimal places.)
What is the probability that the dealership will wait at least 2 year? (Round your
answer to 4 decimal places.)
What is the probability that the dealership will wait at least 4 months but not more
than 1 year? (Round your answer to 4 decimal places.)
Stat 201 Homework 4 Part I Chapters 1 and 2
1 Statistics is the science of collecting, organizing, analyzing, interpreting, and
presenting data.
True
False
2 Inferential statistics refers to generalizing from a sample to a population,
estimating unknown parameters, drawing conclusions, and making decisions.
True
False
3 Descriptive statistics refers to summarizing data rather than generalizing about
the population.
True
False
4 Estimating parameters and testing hypotheses are important aspects of
descriptive statistics.
True
False
5 Empirical data are collected through observations and/or experiments.
True
False
6 Statistical challenges include imperfect data, practical constraints, and ethical
dilemmas.
True
False
7 The science of statistics tells us whether the sample evidence is convincing.
True
False
8 Because 25 percent of the students in my morning statistics class watch eight or
more hours of television a week, I conclude that 25 percent of all students at the
university watch eight or more hours of television a week. The most important
logical weakness of this conclusion would be:
relying on any sample instead of surveying every student.
using a sample that may not be representative of all students.
failing to correct for unconscious interviewer bias.
assuming cause and effect where none exists.
9 Categorical data have values that are described by words rather than numbers.
True
False
10 Numerical data can be either discrete or continuous.
True
False
11 The number of planes per day that land at an airport is an example of discrete
data.
True
False
12 When the population is large, a sample estimate is usually preferable to a
census.
True
False
13 A sampling frame is used to identify the target population in a statistical study.
True
False
14 A random sample is one in which the:
probability that an item is selected for the sample is the same for all population
items.
population items are selected haphazardly by experienced workers.
items to be selected from the population are specified based on expert judgment.
probability of selecting a population item depends on the item’s data value.
Each item must have the same chance of being picked if the sample is random.
15 A binary variable (also called a dichotomous variable or dummy variable) has:
only two possible values.
continuous scale values.
rounded data values.
ordinal or interval values.
Stat 201 Homework 5 Chapter 4
1 The midrange is not greatly affected by outliers.
True
False
2 The second quartile is the same as the median.
True
False
3 A trimmed mean may be preferable to a mean when a data set has extreme
values.
True
False
4 Given the data set 10, 5, 2, 6, 3, 4, 20, the median value is 5.
True
False
5 In a left-skewed distribution, we expect that the median will be greater than the
mean.
True
False
6 Referring to this graph of ice cream fat content, the second quartile is about 61.
True
False
7 In calculating the sample variance, the sum of the squared deviations around the
mean is divided by n – 1 to avoid underestimating the unknown population
variance.
True
False
8 Which is not a characteristic of the standard deviation?
It is always the square root of the variance.
It is not applicable when data are continuous.
It can be calculated when the data contain negative or zero values.
Its physical interpretation is not as easy as the MAD.
9 If samples are from a normal distribution with μ = 100 and σ = 10, we expect:
about 68 percent of the data within 90 to 110.
almost all the data within 80 to 120.
about 95 percent of the data within 70 to 130.
about half the data to exceed 75.
10 In a sample of 10,000 observations from a normal population, how many would
you expect to lie beyond three standard deviations of the mean?
None of them
About 27
About 100
About 127
Stat 201 Homework 6 Confidence Interval
1 Find the interval [ ] within which 95 percent of the sample means
would be expected to fall, assuming that each sample is from a normal population.
(a) μ = 184, σ = 21, n = 40. (Round your answers to 2 decimal places.)
μ = 931, σ = 20, n = 8. (Round your answers to 2 decimal places.)
μ = 66, σ = 2, n = 30. (Round your answers to 3 decimal places.)
2 The fuel economy of a 2011 Lexus RX 350 2WD 6 cylinder 3.5 L automatic
5−speed using premium fuel is a normally distributed random variable with a mean
of μ = 21.5 MPG and a standard deviation of σ = 2.75 MPG.
What is the standard error of , the mean from a random sample of 9 fill−ups by one
driver? (Round your answer to 4 decimal places.)
Within what interval would you expect the sample mean to fall, with 95 percent
probability? (Round your answers to 4 decimal places.)
Concerns about climate change and CO2 reduction have initiated the commercial
production of blends of biodiesel (e.g., from renewable sources) and petrodiesel
(from fossil fuel). Random samples of 32 blended fuels are tested in a lab to
ascertain the bio/total carbon ratio.
(a) If the true mean is 0.913 with a standard deviation of 0.004, within what
interval will 98 percent of the sample means fall? (Round your answers to 4
decimal places.)
(b) If the true mean is 0.913 with a standard deviation of 0.004, what is the
sampling distribution of ?
Exactly Normal with μ = 0.913 and σ = 0.004.
Approximately Normal with μ = 0.913 and σ = 0.004.
Exactly Normal with μ = 0.913 and
Approximately Normal with μ = 0.913 and
(c) Which theorem did you use to answer part (b)?
Pythagorean Theorem
Law of Large Numbers
Chebyshev’s Theorem
Central Limit Theorem
6 Find a confidence interval for μ assuming that each sample is from a normal
population. (Round the value of t to 3 decimal places and your final answers to 2
decimal places.)
= 23, s = 2, n = 7, 90 percent confidence.
(b) = 40, s = 4, n = 16, 99 percent confidence.
(c) = 116, s = 11, n = 26, 95 percent confidence.
A random sample of 23 items is drawn from a population whose standard deviation
is unknown. The sample mean is = 770 and the sample standard deviation is s = 25.
Use Appendix D to find the values of Student’s t.
Construct an interval estimate of μ with 95 percent confidence. (Round your
critical t-value to 3 decimal places. Round your answers to 3 decimal places.)
Construct an interval estimate of μ with 95 percent confidence, assuming that s =
50. (Round your critical t-value to 3 decimal places. Round your answers to 3
decimal places.)
Construct an interval estimate of μ with 95 percent confidence, assuming that s =
100. (Round your critical t-value to 3 decimal places. Round your answers to 3
decimal places.)
(d) Describe how the confidence interval changes as s increases.
The interval stays the same as s increases.
The interval gets narrower as s increases.
The interval gets wider as s increases.
The interval gets wider as s decreases.
Stat 201 Homework 7 Hypothesis Testing
1 The level of significance refers to the probability of making a Type I error.
True
False
2 A Type I error can only occur if you reject H0.
True
False
3 In hypothesis testing we cannot prove a null hypothesis is true.
True
False
4 Compared to using α = .01, choosing α = .001 will make it less likely that a true
null hypothesis will be rejected.
True
False
5 A two-tailed hypothesis test for H0: μ = 15 at α = .10 is analogous to asking if a
90 percent confidence interval for μ contains 15.
True
False
6 For a given sample size and α level, the Student’s t value always exceeds the z
value.
True
False
7 If we desire α = .10, then a p-value of .13 would lead us to reject the null
hypothesis.
True
False
8 The p-value is the probability of the sample result (or one more extreme)
assuming H0 is true.
True
False
9 A null hypothesis is rejected when the calculated p-value is less than the critical
value of the test statistic.
True
False
10 In a right-tailed test, the null hypothesis is rejected when the value of the test
statistic exceeds the critical value.
True
False
11 The critical value of a hypothesis test is based on the researcher’s selected level
of significance.
True
False
12 If the null and alternative hypotheses are H0: μ ≤ 100 and H1: μ > 100, the test
is right-tailed.
True
False
13 If the hypothesized proportion is π0 = .025 in a sample of size 120, it is safe to
assume normality of the sample proportion p.
True
False
14 In the hypothesis H0: π = π0, the value of π0 is derived from the sample.
True
False
15 For a given sample size, when we increase the probability of Type I error, the
probability of a Type II error:
remains unchanged.
increases.
decreases.
is impossible to determine without more information.
The sodium content of a popular sports drink is listed as 230 mg in a 32-oz bottle.
Analysis of 13 bottles indicates a sample mean of 238.3 mg with a sample standard
deviation of 20.9 mg.
(a) State the hypotheses for a two-tailed test of the claimed sodium content.
H0: µ ≥ 230 vs. H1: < 230 H0: µ ≤ 230 vs. H1: > 230
H0: µ = 230 vs. H1: µ ≠ 230
Calculate the t test statistic to test the manufacturer’s claim. (Round your answer to
4 decimal places.)
At the 2 percent level of significance (α = 0.02) does the sample contradict the
manufacturer’s claim?
Use Excel to find the p-value and compare it to the level of significance. (Round
your answer to 4 decimal places.)
Did you come to the same conclusion as you did in part (c)?
A digital camcorder repair service has set a goal not to exceed an average of 5
working days from the time the unit is brought in to the time repairs are completed.
A random sample of 12 repair records showed the following repair times (in days):
9, 9, 5, 6, 5, 7, 6, 3, 7, 9, 8, 4.
(a) H0: μ ≤ 5 days versus H1: μ > 5 days. At α = .05, choose the right option.
Reject H0 if tcalc < 1.7960 Reject H0 if tcalc >1.7960
Calculate the Test statistic. (Round your answer to 3 decimal places.)
The null hypothesis should be rejected.
The average repair time is longer than 5 days.
At α = .05 is the goal being met?
A web-based company has a goal of processing 95 percent of its orders on the
same day they are received. If 516 out of the next 534 orders are processed on the
same day, would this prove that they are exceeding their goal, using α = .025?
(a) H0: π ≤ .95 pages versus H1: π > .95. Choose the right option.
Reject H0 if zcalc > 1.96
Reject H0 if zcalc < 1.96 (b) Calculate the Test statistic. (Round your sample
proportion to five decimal places and final answer to 3 decimal places.) (c-1) The
null hypothesis should be rejected. (c-2) The true proportion is greater than .95. (c3) The company is exceeding its goal.
Stat 201 Homework 8 Simple Linear Regression
1. The correlation coefficient r always has the same sign as b1 in Y = b0 + b1X.
True
False
2 The least squares regression line is obtained when the sum of the squared
residuals is minimized.
True
False
3. In least-squares regression, the residuals e1, e2, . . . , en will always have a zero
mean.
True
False
4. If R2 = .36 in the model Sales = 268 + 7.37 Ads, then Ads explains 36 percent
of the variation in Sales.
True
False
5. The ordinary least squares regression line always passes through the point .
True
False
6. If SSR is 1800 and SSE is 200, then R2 is .90.
True
False
7. The total sum of squares (SST) will never exceed the regression sum of squares
(SSR).
True
False
8. In a simple regression, there are n – 2 degrees of freedom associated with the
error sum of squares (SSE).
True
False
9. In a simple regression, the F statistic is calculated by taking the ratio of MSR to
the MSE.
True
False
10. The coefficient of determination is the percentage of the total variation in the
response variable Y that is explained by the predictor X.
True
False
11. The regression equation NetIncome = 2,417 + 0.0414 Revenue was estimated
from a sample of 100 leading world companies (variables are in millions of
dollars).
Calculate the residual for the x, y pair ($45,753, $4,901). (Negative value should
be indicated by a minus sign. Round your answer to 4 decimal places.)
12.(a2) Did the regression equation underestimate or overestimate the net income?
The regression equation overestimated the net income.
The regression equation underestimated the net income.
13. (b1) Calculate the residual for the x, y pair ($63,293, $4,070).(Negative value
should be indicated by a minus sign. Round your answer to 4 decimal places.)
14. (b2) Did the regression equation underestimate or overestimate the net income?
The regression equation overestimated the net income.
The regression equation underestimated the net income.
Stat 201 Midterm Exam
1 Statistics is the science of collecting, organizing, analyzing, interpreting, and
presenting data.
True
False
2 The second quartile is the same as the median.
True
False
3 A trimmed mean may be preferable to a mean when a data set has extreme
values.
True
False
4 Given the data set 10, 5, 2, 6, 3, 4, 20, the median value is 5.
True
False
5 In calculating the sample variance, the sum of the squared deviations around the
mean is divided by n – 1 to avoid underestimating the unknown population
variance.
True
False
6 The position of the median is:
n/2 in any sample.
n/2 if n is even.
n/2 if n is odd.
(n + 1)/2 in any sample.
7 Which is a characteristic of the trimmed mean as a measure of center?
It is similar to the mean if there are offsetting high and low extremes.
It is especially helpful in a small sample.
It does not require sorting the sample.
It is basically the same as the midrange.
8
A biometric security device using fingerprints erroneously refuses to admit 2 in
1,200 authorized persons from a facility containing classified information. The
device will erroneously admit 2 in 1,010,000 unauthorized persons. Assume that
95 percent of those who seek access are authorized.
If the alarm goes off and a person is refused admission, what is the probability that
the person was really authorized? (Round your answer to 5 decimal places.)
9 A sample space is the set of all possible outcomes in an experiment.
True
False
10 The probability of the union of two events P(A or B) can exceed one.
True
False
11 Two events A and B are independent if P(A | B) is the same as P(A).
True
False
12 For any event A, the probability of A is always 0 ≤ P(A) ≤ 1.
True
False
13 If events A and B are mutually exclusive, the joint probability of the events is
zero.
True
False
14 If A and B are mutually exclusive events, then P(A ∩ B) = P(A) + P(B).
True
False
15 If P(A | B) = 0.40 and P(B) = 0.30, find P(A ∩ B).
.171
.525
.571
.120
16 A company is producing two types of ski goggles. Thirty percent of the
production is of type A, and the rest is of type B. Five percent of all type A goggles
are returned within 10 days after the sale, whereas only two percent of type B are
returned. If a pair of goggles is returned within the first 10 days after the sale, the
probability that the goggles returned are of type B is:
.014.
.140.
.070.
.483.
17
Half of a set of the parts are manufactured by machine A and half by machine B.
Ten percent of all the parts are defective. One percent of the parts manufactured on
machine A are defective.
Find the probability that a part was manufactured on machine A, given that the part
is defective. (Round your answer to 4 decimal places.)
18
Car security alarms go off at a mean rate of 2.8 per hour in a large Costco parking
lot.
Find the probability that in an hour there will be (Round your answers to 4 decimal
places.)
19 Past insurance company audits have found that 1 percent of dependents claimed
on an employee’s health insurance actually are ineligible for health benefits. An
auditor examines a random sample of 8 claimed dependents.
(a) What is the probability that all are eligible? (Round your answer to 4 decimal
places.)
What is the probability that at least one is ineligible? (Round your answer to 4
decimal places.)
20 Which model best describes the number of incorrect fare quotations by a welltrained airline ticket agent between 2 p.m. and 3 p.m. on a particular Thursday.
Binomial
Poisson
Hypergeometric
Geometric
21 On a randomly chosen Wednesday, which probability model would you use to
describe the number of convenience store robberies in Los Angeles?
Binomial
Poisson
Hypergeometric
Geometric
22 A continuous uniform distribution is always symmetric.
True
False
23 If arrivals follow a Poisson distribution, waiting times follow the exponential
distribution.
True
False
24 The mean, median, and mode of a normal distribution will always be the same.
True
False
25 A machine dispenses water into a glass. Assuming that the amount of water
dispensed follows a continuous uniform distribution from 10 ounces to 16 ounces,
the average amount of water dispensed by the machine is:
12 ounces.
13 ounces.
14 ounces.
16 ounces.
26 A machine dispenses water into a glass. Assuming that the amount of water
dispensed follows a continuous uniform distribution from 10 ounces to 16 ounces,
what is the probability that 13 or more ounces will be dispensed in a given glass?
.1666
.3333
.5000
.6666
27 A student’s grade on an examination was transformed to a z value of 0.67.
Assuming a normal distribution, we know that she scored approximately in the top:
15 percent.
50 percent.
40 percent.
25 percent.
28
Automobile warranty claims for engine mount failure in a Troppo Malo 2000 SE
are rare at a certain dealership, occurring at a mean rate of 0.12 claim per month.
What is the probability that the dealership will wait at least 6 months until the next
claim? (Round your answer to 4 decimal places.)
What is the probability that the dealership will wait at least a year? (Round your
answer to 4 decimal places.)
What is the probability that the dealership will wait at least 2 year? (Round your
answer to 4 decimal places.)
What is the probability that the dealership will wait at least 6 months but not more
than 1 year? (Round your answer to 4 decimal places.)
29 In Melanie’s Styling Salon, the time to complete a simple haircut is normally
distributed with a mean of 25 minutes and a standard deviation of 4 minutes. What
percent of customers require less than 32 minutes for a simple haircut?
95.99 percent
99.45 percent
97.72 percent
45.99 percent
30 In Melanie’s Styling Salon, the time to complete a simple haircut is normally
distributed with a mean of 25 minutes and a standard deviation of 4 minutes. For a
simple haircut, the middle 90 percent of the customers will require:
between 18.4 and 31.6 minutes.
between 19.9 and 30.1 minutes.
between 20.0 and 30.0 minutes.
between 17.2 and 32.8 minutes.
31 Of the patients of a hospital, 40% of the redhead have had skin cancer, and 10%
of the non-redhead have had skin cancer. Also 20% of the patients are redheads.
Patient Lee has skin cancer, then what is the probability that he is a redhead?
32. A gambler has in his pocket “two” fair coins and “two” two-headed coin. He
selects one of the coins at random; when he flips it, it shows heads. What is the
probability that it is a fair coin?
Stat 201 Quiz 1
1A sample space is the set of all possible outcomes in an experiment.
True
False
2The sum of all the probabilities of simple events in a sample space equals one.
True
False
3The general law of addition for probabilities says P(A or B) = P(A) + P(B) – P(A
∩ B)
True
False
4Two events A and B are independent if P(A | B) is the same as P(A).
True
False
5 If events A and B are mutually exclusive, the joint probability of the events is
zero.
True
False
6 If P(A) = 0.50, P(B) = 0.30, and P(A ∩ B) = 0.15, then A and B are independent
events.
True
False
7 A biometric security device using fingerprints erroneously refuses to admit 2 in
1,500 authorized persons from a facility containing classified information. The
device will erroneously admit 2 in 1,013,000 unauthorized persons. Assume that
95 percent of those who seek access are authorized.
If the alarm goes off and a person is refused admission, what is the probability that
the person was really authorized? (Round your answer to 5 decimal places.)
8 A random variable is a function or rule that assigns a numerical value to each
outcome in the sample space of a stochastic (chance) experiment.
True
False
9 The expected value of a discrete random variable E(X) is the sum of all X values
weighted by their respective probabilities.
True
False
10 The Poisson distribution describes the number of occurrences within a
randomly chosen unit of time or space.
True
False
11 The probability that an American CEO can transact business in a foreign
language is .30. Eleven American CEOs are chosen at random.
(a) What is the probability that none can transact business in a foreign language?
(Round your answer to 4 decimal places.)
(b) What is the probability that at least two can transact business in a foreign
language? (Round your answer to 4 decimal places.)
(c) What is the probability that all 11 can transact business in a foreign language?
(Round your answer to 10 decimal places.)
12 Car security alarms go off at a mean rate of 3.0 per hour in a large Costco
parking lot.
Find the probability that in an hour there will be (Round your answers to 4 decimal
places.)
13 If arrivals follow a Poisson distribution, waiting times follow the exponential
distribution.
True
False
14 The exponential distribution is continuous and the Poisson distribution is
discrete, yet the two distributions are closely related.
True
False
15 A random variable X is best described by a continuous uniform distribution
from 20 to 45 inclusive. What is P(30 ≤ X ≤ 40)?
.20
.40
.60
.80
16 The fracture strength of a certain type of manufactured glass is normally
distributed with a mean of 541 MPa with a standard deviation of 18 MPa.
(a) What is the probability that a randomly chosen sample of glass will break at
less than 541 MPa? (Round your answer to 2 decimal places.)
What is the probability that a randomly chosen sample of glass will break at more
than 565 Mpa? (Round your answer to 4 decimal places.)
What is the probability that a randomly chosen sample of glass will break at less
than 579 MPa? (Round your answer to 4 decimal places.)
17
Jim’s systolic blood pressure is a random variable with a mean of 140 mmHg and a
standard deviation of 12 mmHg. For Jim’s age group, 140 is the threshold for high
blood pressure.
Assume the data given follows the normal probability distribution.
(a) If Jim’s systolic blood pressure is taken at a randomly chosen moment, what is
the probability that it will be 130 or less? (Round the value of z to 2 decimals. Use
Appendix C-2 to find probabilities. Round your final answer to 4 decimals.)
(b) If Jim’s systolic blood pressure is taken at a randomly chosen moment, what is
the probability that it will be 173 or more? (Round the value of z to 2 decimals.
Use Appendix C-2 to find probabilities. Round your final answer to 4 decimals.)
(c) If Jim’s systolic blood pressure is taken at a randomly chosen moment, what is
the probability that it will be between 111 and 160? (Round the value of z to 2
decimals. Use Appendix C-2 to find probabilities. Round your final answer to 4
decimals.)
Stat 201 Quiz 2
1 A random sample of 24 lunch orders at Noodles and Company showed a mean
bill of $12.47 with a standard deviation of $6.58. Find the 98 percent confidence
interval for the mean bill of all lunch orders. (Round your answers to 4 decimal
places.)
2 The Environmental Protection Agency (EPA) requires that cities monitor over 80
contaminants in their drinking water. Samples from the Lake Huron Water
Treatment Plant gave the results shown here. Only the range is reported, not the
mean (presumably the mean would be the midrange).
Use the sample information x = 36, σ = 7, n = 20 to calculate the following
confidence intervals for μ assuming the sample is from a normal population.
90 percent confidence. (Round your answers to 4 decimal places.)
95 percent confidence. (Round your answers to 4 decimal places.)
99 percent confidence. (Round your answers to 4 decimal places.)
(d) Describe how the intervals change as you increase the confidence level.
The interval gets narrower as the confidence level increases.
The interval gets wider as the confidence level increases.
The interval stays the same as the confidence level increases.
The interval gets wider as the confidence level decreases.
7.
The city fuel economy of a 2009 Toyota 4Runner 2WD 6 cylinder 4 L automatic 5speed using regular gas is a normally distributed random variable with a range 26
MPG to 31 MPG.
(a) Estimate the standard deviation using Method 3 (the Empirical Rule for a
normal distribution). (Round your answer to 4 decimal places.)
What sample size is needed to estimate the mean with 90 percent confidence and
an error of ± 0.25 MPG? (Enter your answer as a whole number (no decimals). Use
a z-value taken to three decimal places in your calculations.)
8 Inspection of a random sample of 27 aircraft showed that 16 needed repairs to fix
a wiring problem that might compromise safety.
How large a sample would be needed to estimate the true proportion of jets with
the wiring problem, with 98 percent confidence and an error of ± 8 percent? (Enter
your answer as a whole number (no decimals). Use a z-value taken to three
decimal places in your calculations.)
Would the airline actually conduct further sampling, or just inspect all the planes?
Stat 201 Quiz 3
GreenBeam Ltd. claims that its compact fluorescent bulbs average no more than
3.6 mg of mercury. A sample of 25 bulbs shows a mean of 3.65 mg of mercury.
1 (a) State the hypotheses for a right-tailed test, using GreenBeam’s claim as the
null hypothesis about the mean.
Assuming a known standard deviation of 0.16 mg, calculate the z test statistic to
test the manufacturer’s claim. (Round your answer to 2 decimal places.)
At the 10 percent level of significance (α = 0.1) does the sample exceed the
manufacturer’s claim?
Find the p-value. (Round your answer to 4 decimal places.)
The average weight of a package of rolled oats is supposed to be at least 16 ounces.
A sample of 18 packages shows a mean of 15.81 ounces with a standard deviation
of 0.48 ounce.
At the 5 percent level of significance, is the true mean smaller than the
specification? Clearly state your hypotheses and decision rule.
If α = 0.01, we would have
Use Excel to find the p-value. (Round your answer to 4 decimal places.)
In a recent survey, 10 percent of the participants rated Pepsi as being “concerned
with my health.” PepsiCo’s response included a new “Smart Spot” symbol on its
products that meet certain nutrition criteria, to help consumers who seek more
healthful eating options.
Suppose a follow-up survey showing that 50 of 400 persons now rate Pepsi as
being “concerned with my health”, calculate the z statistic. (Round your answer to
3 decimal places.)
At α = 0.05, would a follow-up survey showing that 50 of 400 persons now rate
Pepsi as being “concerned with my health” provide sufficient evidence that the
percentage has increased?