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Final Exam Review
Name___________________________________
Find the indicated probability.
1) A multiple choice test has 7 questions each of which has 5 possible answers, only one of which is
correct. If Judy, who forgot to study for the test, guesses on all questions, what is the probability that
she will answer exactly 3 questions correctly?
2) A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean
of 200 and a standard deviation of 50. If an applicant is randomly selected, find the probability of a
rating that is between 170 and 220.
3) A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean
of 200 and a standard deviation of 50. If an applicant is randomly selected, find the probability of a
rating that is between 200 and 275.
4) In one town, 44% of all voters are Democrats. If two voters are randomly selected for a survey, find
the probability that they are both Democrats. Round to the nearest thousandth if necessary.
5) You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing
cards. Find the probability that both cards are black. Express your answer as a simplified fraction.
6) In one region, the September energy consumption levels for single-family homes are found to be
normally distributed with a mean of 1050 kWh and a standard deviation of 218 kWh. For a randomly
selected home, find the probability that the September energy consumption level is between 1100
kWh and 1225 kWh.
7) The brand name of a certain chain of coffee shops has a 46% recognition rate in the town of
Coffleton. An executive from the company wants to verify the recognition rate as the company is
interested in opening a coffee shop in the town. He selects a random sample of 8 Coffleton residents.
Find the probability that exactly 4 of the 8 Coffleton residents recognize the brand name.
8) The table below describes the smoking habits of a group of asthma sufferers.
If one of the 963 people is randomly selected, find the probability that the person is a man or a heavy
smoker.
9) The diameters of bolts produced by a certain machine are normally distributed with a mean of 0.30
inches and a standard deviation of 0.01 inches. What percentage of bolts will have a diameter greater
than 0.32 inches?
10) A multiple choice test has 12 questions each of which has 4 possible answers, only one of which is
correct. If Judy, who forgot to study for the test, guesses on all questions, what is the probability that
she will answer exactly 3 questions correctly?
11) The table below describes the smoking habits of a group of asthma sufferers.
If one of the 1127 people is randomly selected, find the probability that the person is a man or a heavy
smoker.
Find the value of the linear correlation coefficient r.
12)
13) Managers rate employees according to job performance and attitude. The results for several
randomly selected employees are given below.
14) The paired data below consist of the costs of advertising (in thousands of dollars) and the number
of products sold (in thousands):
15)
Use the given information to find the minimum sample size required to estimate an unknown
population mean μ.
16) How many business students must be randomly selected to estimate the mean monthly earnings
of business students at one college? We want 95% confidence that the sample mean is within $ 128 of
the population mean, and the population standard deviation is known to be $536.
Solve the problem.
17) A newspaper article about the results of a poll states: "In theory, the results of such a poll, in 99
cases out of 100 should differ by no more than 5 percentage points in either direction from what
would have been obtained by interviewing all voters in the United States." Find the sample size
suggested by this statement.
18) A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean
of 200 and a standard deviation of 50.
a) If 40 different applicants are randomly selected, find the probability that their mean is
above 215.
b) Would it be considered unusual for a group of 40 randomly selected applicants to have a
mean rating greater than 215?
19) In a certain population, body weights are normally distributed with a mean of 152 pounds and a
standard deviation of 26 pounds. How many people must be surveyed if we want to estimate the
percentage who weigh more than 180 pounds? Assume that we want 96% confidence that the error is
no more than 4 percentage points.
20) The annual precipitation amounts in a certain mountain range are normally distributed with a
mean of 107 inches, and a standard deviation of 12 inches.
a) What is the probability that the mean annual precipitation during 36 randomly picked
years will be less than 109.8 inches?
b) Would it be considered unusual for 36 randomly picked years to have a mean less than
109.8 inches?
21) In one region, the September energy consumption levels for single-family homes are found to be
normally distributed with a mean of 1050 kWh and a standard deviation of 218 kWh
a) If 50 different homes are randomly selected, find the probability that their mean energy
consumption level for September is greater than 1075 kWh
b) Would it be considered unusual for a group of 50 different single-family homes to have a
mean energy consumption level for September that is greater than 1075 kWh?
Determine which score corresponds to the higher relative position.
22) Which is better, a score of 92 on a test with a mean of 71 and a standard deviation of 15, or a score
of 688 on a test with a mean of 493 and a standard deviation of 150?
23) Which score has the highest relative position: a score of 32 on a test for which the mean was 26
and the standard deviation was 10, a score of 5.7 on a test for which the mean was 4.7 and the
standard deviation was 1.3 or a score of 394.5 on a test for which the mean was 374 and the standard
deviation was 41?
24) Which score has a higher relative position, a score of 60 on a test for which the mean was 53 and
the standard deviation was 10 or a score of 240.3 on a test for which the mean was 206 and the
standard deviation was 49?
Assume that a simple random sample has been selected from a normally distributed population
and test the given claim. Use either the traditional method or P-value method as indicated.
Identify the null and alternative hypotheses, test statistic, critical value(s) or P-value (or range of
P-values) as appropriate, and state the final conclusion that addresses the original claim.
25) A researcher wants to test the claim that convicted burglars spend an average of 18.7 months in
jail. She takes a random sample of 11 such cases from court files and finds that the sample has a mean
of 20.6 months. The standard deviation of the sample is 7.8 months. Test the claim that μ = 18.7
months at the 0.05 significance level. Use the traditional method of testing hypotheses.
26) A large software company gives job applicants a test of programming ability and the mean for
that test has been 160 in the past. Twenty-five job applicants are randomly selected from one large
university and they produce a mean score and standard deviation of 183 and 12, respectively. Use a
0.05 level of significance to test the claim that this sample comes from a population with a mean score
greater than 160. Use the P-value method of testing hypotheses.
27) A manufacturer makes ball bearings that are supposed to have a mean weight of 30 g. A retailer
suspects that the mean weight is actually less than 30 g. The mean weight for a random sample of 16
ball bearings is 28.4 g with a standard deviation of 4.5 g. At the 0.05 significance level, test the claim
that the sample comes from a population with a mean weight less than 30 g. Use the traditional
method of testing hypotheses.
28) A public bus company official claims that the mean waiting time for bus number 14 during peak
hours is less than 10 minutes. Karen took bus number 14 during peak hours on 18 different occasions.
Her mean waiting time was 7.6 minutes with a standard deviation of 2.3 minutes. At the 0.01
significance level, test the claim that the mean waiting time is less than 10 minutes. Use the P-value
method of testing hypotheses.
Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most
appropriate.
29) Temperatures of the ocean at various depths.
30) Nationalities of survey respondents.
31) Salaries of college professors.
32) Survey responses of "good, better, best".
Use the given data to find the best predicted value of the response variable.
33) Ten pairs of data yield r = 0.003 and the regression equation 𝑦̂ = 2 + 3𝑥. Also, 𝑦̅ = 5.0. What is
the best predicted value of y for 𝑥 = 2?
34) Eight pairs of data yield r = 0.708 and the regression equation 𝑦̂ = 55.8 + 2.79𝑥. Also, 𝑦̅ = 71.125.
What is the best predicted value of y for 𝑥 = 6.8?
35) Based on the data from six students, the regression equation relating number of hours of
preparation (x) and test score (y) is 𝑦̂ = 67.3 + 1.07𝑥. The same data yield 𝑟 = 0.224 and 𝑦̅ = 75.2.
What is the best predicted test score for a student who spent 4 hours preparing for the test?
36) Eight pairs of data yield r = 0.708 and the regression equation 𝑦̂ = 55.8 + 2.79𝑥. Also, 𝑦̅ = 71.125.
What is the best predicted value of y for 𝑥 = 9.7?
37) The regression equation relating dexterity scores (x) and productivity scores (y) for the employees
of a company is 𝑦̂ = 5.50 + 1.91𝑥. Ten pairs of data were used to obtain the equation. The same data
yield 𝑟 = 0.986 and 𝑦̅ = 56.3. What is the best predicted productivity score for a person whose
dexterity score is 32?
38) Six pairs of data yield r = 0.444 and the regression equation 𝑦̂ = 5𝑥 + 2. Also, 𝑦̅ = 18.3. What is
the best predicted value of y for 𝑥 = 5?
39) Thirty randomly selected students took the calculus final. The sample mean was 83 and the thirty
students had a standard deviation of 13.5.
a) Construct a 99% confidence interval for the mean score of all students.
b) Interpret the confidence interval.
40) Many states are carefully considering steps that would help them collect sales taxes on items
purchased through the Internet. How many randomly selected sales transactions must be surveyed to
determine the percentage that transpired over the Internet? Assume that we want to be 95% confident
that the sample percentage is within five percentage points of the true population percentage for all
sales transactions.
Find the indicated probability. Express your answer as a simplified fraction unless otherwise
noted.
41) The following table contains data from a study of two airlines which fly to Small Town, USA.
If one of the 87 flights is randomly selected, find the probability that the flight selected is an Upstate
Airlines flight given that it was late.
42) The following table contains data from a study of two airlines which fly to Small Town, USA.
If one of the 87 flights is randomly selected, find the probability that the flight selected arrived on
time given that it was an Upstate Airlines flight.
43) The table below shows the soft drinks preferences of people in three age groups.
If one of the 255 subjects is randomly selected, find the probability that the person drinks root beer
given that they are over 40.
Use the given data to construct a frequency distribution AND a relative frequency distribution.
44) Lori asked 24 students how many hours they had spent doing homework during the previous
week. The results are shown below.
10
11
10
8
10
10
14
13
10
9
13
11
11
13
10
11
13
10
11
13
11
13
13
8
Construct a frequency distribution AND relative frequency distribution. Use 4 classes, a class width
of 2 hours, and a lower limit of 8 for class 1.
45) Kevin asked some of his friends how many hours they had worked during the previous week at
their after-school jobs. The results are shown below.
6
5
6
3
6
6
9
8
6
3
8
5
5
8
6
5
8
6
5
8
5
8
8
3
Construct a frequency distribution AND relative frequency distribution. Use 4 classes, a class width
of 2 hours, and a lower limit of 3 for class 1.
46) Lori asked 24 students how many hours they had spent doing homework during the previous
week. The results are shown below.
11
11
11
9
11
11
15
13
11
8
13
11
11
13
11
11
13
11
11
13
11
13
13
9
Construct a frequency distribution AND relative frequency distribution. Use 4 classes, a class width
of 2 hours, and a lower limit of 8 for class 1.
Use the pie chart to solve the problem.
47) The pie chart below gives the number of students in the residence halls at the state university.
Which residence hall has the highest number of students?
Use the confidence level and sample data to find a confidence interval for estimating the
population μ. Round your answer to the same number of decimal places as the sample mean.
48) A random sample of 104 light bulbs had a mean life of 543 hours with a population standard
deviation of 26 hours. Construct a 90% confidence interval for the mean life, μ, of all light bulbs of
this type.
a) Construct a 90% confidence interval for the mean life of all light bulbs of this type.
b) Interpret the confidence interval.
Use the given degree of confidence and sample data to construct a confidence interval for the
population mean μ. Assume that the population has a normal distribution. Round your answer
to the same number of decimal places as the sample mean.
49) A laboratory tested 82 chicken eggs and found that the mean amount of cholesterol was 228
milligrams. The population standard deviation is 19.0 milligrams. Construct a 95% confidence
interval for the true mean cholesterol content, μ, of all such eggs.
a) Construct a 95% confidence interval for the true mean cholesterol content, μ, of all such
eggs.
b) Interpret the confidence interval.
Use the confidence level and sample data to find a confidence interval for estimating the
population μ. Round your answer to the same number of decimal places as the sample mean.
50) A random sample of 105 light bulbs had a mean life of 441 hours with a population standard
deviation of 40 hours. Construct a 90% confidence interval for the mean life, μ, of all light bulbs of
this type.
Use the given degree of confidence and sample data to construct a confidence interval for the
population mean μ. Assume that the population has a normal distribution. Round your answer
to the same number of decimal places as the sample mean.
51) A group of 59 randomly selected students have a mean score of 29.5 on a placement test. The
population standard deviation is 5.2 on a placement test. What is the 90% confidence interval for the
mean score, μ, of all students taking the test?
a) Construct a 90% confidence interval for the mean score of all students.
b) Interpret the confidence interval.
Use the given degree of confidence and sample data to construct a confidence interval for the
population proportion p.
52) A survey of 300 union members in New York State reveals that 112 favor the Republican
candidate for governor. Construct the 98% confidence interval for the true population proportion of
all New York State union members who favor the Republican candidate.
53) When 328 college students are randomly selected and surveyed, it is found that 122 own a car.
Find a 99% confidence interval for the true proportion of all college students who own a car.
54) Of 346 items tested, 12 are found to be defective. Construct the 98% confidence interval for the
proportion of all such items that are defective.
Use critical thinking to develop an alternative conclusion.
55) A study shows that adults who work at their desk all day weigh more than those who do not.
Conclusion: Desk jobs cause people to gain weight.
56) A study of achievement scores by sixth-grade students on a standardized math test showed the
three top scorers were all gifted piano players. Conclusion: Playing the piano leads to mathematical
achievement.
Find the indicated probability. Round to three decimal places.
57) A car insurance company has determined that 9% of all drivers were involved in a car accident
last year. Among the 14 drivers living on one particular street, 3 were involved in a car accident last
year. If 14 drivers are randomly selected, what is the probability of getting 3 or more who were
involved in a car accident last year?
58) The participants in a television quiz show are picked from a large pool of applicants with
approximately equal numbers of men and women. Among the last 11 participants there have been
only 2 women. If participants are picked randomly, what is the probability of getting 2 or fewer
women when 11 people are picked?
Determine whether the given procedure results in a binomial distribution. If not, state the reason
why.
59) Rolling a single die 26 times, keeping track of the numbers that are rolled.
60) Choosing 8 marbles from a box of 40 marbles (20 purple, 12 red, and 8 green) one at a time with
replacement, keeping track of the number of red marbles chosen.
Use critical thinking to address the key issue.
61) A questionnaire is sent to 10,000 persons. 5,000 responded to the questionnaire. 3,000 of the
respondents say that they "love chocolate ice cream". We conclude that 60% of people love chocolate
ice cream. What is wrong with this survey?
62) A researcher wished to gauge public opinion on gun control. He randomly selected 1000 people
from among registered voters and asked them the following question: "Do you believe that gun
control laws which restrict the ability of Americans to protect their families should be eliminated?".
Identify the abuse of statistics and suggest a way the researcher's methods could be improved.
63) For the given data, construct a dot plot. Use the dot plot to describe the shape of the distribution.
0
5
2
9
1
1
7
4
0
3
2
6
0
1
8
4
3
1
1
8
0
2
2
0
5
1
0
2
Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the
null hypothesis, and final conclusion that addresses the original claim.
64) A poll of 1068 adult Americans reveals that 48% of the voters surveyed prefer the Democratic
candidate for the presidency. At the 0.05 level of significance, test the claim that at least half of all
voters prefer the Democrat.
Do one of the following, as appropriate: (a) Find the critical value 𝒛𝜶⁄𝟐, (b) find the critical value
𝒕𝜶⁄𝟐, (c) state that neither the normal nor the t distribution applies.
65) 99%; n = 17; σ is unknown; population appears to be normally distributed.
66) 95%; n = 11; σ is known; population appears to be very skewed.
67) 90%; n =9; σ = 4.2; population appears to be very skewed.
68) 91%; n = 45; σ is known; population appears to be very skewed.
69) For the given data, construct a dot plot. Use the dot plot to describe the shape of the distribution.
9
4
7
0
8
8
2
5
9
6
7
3
9
8
1
5
6
8
8
1
9
7
7
9
4
8
9
7
Express the null hypothesis and the alternative hypothesis in symbolic form. Use the correct
symbol
for the indicated parameter.
70) A psychologist claims that more than 4.1 percent of the population suffers from professional
problems due to extreme shyness. Use p, the true percentage of the population that suffers from
extreme shyness.
71) The owner of a football team claims that the average attendance at games is over 62,900, and he is
therefore justified in moving the team to a city with a larger stadium.
72) A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO,
p, is less than 3 in every one thousand.
73) A history teacher designed a quiz to take 30 minutes to complete. Following are the times (in
minutes) for a randomly selected group of students to finish the quiz.
Find the requested sample statistics (round to 1 decimal place).
43
35
38
35
35
40
45
38
a) Mean
b) Median
c) Mode
d) Range
e) Standard Deviation (SHOW ALL WORK)
f) Based on the data, would you consider 30 minutes enough time for the quiz? Explain
your answer.
Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim.
74) An entomologist writes an article in a scientific journal which claims that fewer than 12 in ten
thousand male fireflies are unable to produce light due to a genetic mutation. Assuming that a
hypothesis test of the claim has been conducted and that the conclusion is to reject the null
hypothesis, state the conclusion in nontechnical terms.
75) A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO,
p, is less than 2 in every ten thousand. Assuming that a hypothesis test of the claim has been
conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in
nontechnical terms.
76) A researcher claims that 62% of voters favor gun control. Assuming that a hypothesis test of the
claim has been conducted and that the conclusion is failure to reject the null hypothesis, state the
conclusion in nontechnical terms.
77) A cereal company claims that the mean weight of the cereal in its packets is at least 14 oz.
Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject
the null hypothesis, state the conclusion in nontechnical terms.
78) Carter Motor Company claims that its new sedan, the Libra, will average better than 30 miles per
gallon in the city. Assuming that a hypothesis test of the claim has been conducted and that the
conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms.
79) Mrs. Osborn designed a test to take 45 minutes to complete. Following are the times (in minutes)
for a randomly selected group of students to finish the test. Find the requested sample statistics
(round to 1 decimal place).
80
35
28
35
35
40
45
38
a) Mean
b) Median
c) Mode
d) Range
e) Standard Deviation (SHOW ALL WORK)
f) Based on the data, would you consider 45 minutes enough time for the test? Explain your
answer.
80) What is the minimum sample size required to estimate the proportion of Lake Sumter State
College students who prefer taking online classes to seated classes with 96% confidence to within
1.5% of the actual proportion?