Download THT 3 STAT spr 2014 For Test 3 review

TAKE HOME TEST STAT 2023 Spring 2014
Name___________________________________
SHOW ALL STEPS AND WORK
Determine if the outcome is unusual. Consider as unusual any result that differs from the mean by more than 2 standard
deviations. That is, unusual values are either less than µ - 2 or greater than µ + 2 .
1) A survey for brand recognition is done and it is determined that 68% of consumers have heard of Dull
Computer Company. A survey of 800 randomly selected consumers is to be conducted. For such groups of 800,
would it be unusual to get 698 consumers who recognize the Dull Computer Company name?
Solve the problem.
2) According to a college survey, 22% of all students work full time. Find the standard deviation for the number of
students who work full time in samples of size 16.
3) A die is rolled 23 times and the number of twos that come up is tallied. If this experiment is repeated many
times, find the standard deviation for the number of twos.
4) On a multiple choice test with 21 questions, each question has four possible answers, one of which is correct. For
students who guess at all answers, find the standard deviation for the number of correct answers.
5) The probability that a radish seed will germinate is 0.7. A gardener plants seeds in batches of 9. Find the mean
for the number of seeds germinating in each batch.
Find the standard deviation, , for the binomial distribution which has the stated values of n and p. Round your answer
to the nearest hundredth.
6) n = 2165; p = 0.63
7) n = 47; p = 0.4
Find the mean, µ, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth.
8) n = 2772; p = 0.63
9) n = 1632; p = 0.57
Find the indicated probability.
10) The brand name of a certain chain of coffee shops has a 54% 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 10 Coffleton residents. Find the probability that exactly
4 of the 10 Coffleton residents recognize the brand name.
11) A multiple choice test has 7 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?
Find the indicated probability. Round to three decimal places.
12) In a certain college, 33% of the physics majors belong to ethnic minorities. If 10 students are selected at random
from the physics majors, that is the probability that no more than 6 belong to an ethnic minority?
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13) Find the probability of at least 2 girls in 7 births. Assume that male and female births are equally likely and that
the births are independent events.
Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability
formula to find the probability of x successes given the probability p of success on a single trial. Round to three decimal
places.
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14) n = 6, x = 3, p =
6
15) n = 10, x = 2, p =
1
3
Determine whether the given procedure results in a binomial distribution. If not, state the reason why.
16) Rolling a single die 57 times, keeping track of the numbers that are rolled.
17) Rolling a single die 47 times, keeping track of the "fives" rolled.
18) Choosing 5 people (without replacement) from a group of 58 people, of which 15 are women, keeping track of
the number of men chosen.
Find the indicated probability. Round to three decimal places.
19) A test consists of 10 true/false questions. To pass the test a student must answer at least 6 questions correctly. If
a student guesses on each question, what is the probability that the student will pass the test?
20) Find the probability of at least 2 girls in 9 births. Assume that male and female births are equally likely and that
the births are independent events.
Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard
deviation 1.
21)
22)
2
Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.
23) Shaded area is 0.0901.
24) Shaded area is 0.8599.
Provide an appropriate response. Round to the nearest hundredth.
25) Find the standard deviation for the given probability distribution.
x P(x)
0 0.12
1 0.07
2 0.21
3 0.30
4 0.30
If z is a standard normal variable, find the probability.
26) The probability that z is less than 1.13
27) The probability that z lies between -1.10 and -0.36
28) P(z > 0.59)
Using the following uniform density curve, answer the question.
29) What is the probability that the random variable has a value greater than 2?
Provide an appropriate response. Round to the nearest hundredth.
30) A police department reports that the probabilities that 0, 1, 2, and 3 burglaries will be reported in a given day
are 0.49, 0.39, 0.08, and 0.04, respectively. Find the standard deviation for the probability distribution. Round
answer to the nearest hundredth.
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Find the indicated probability. Express your answer as a simplified fraction unless otherwise noted.
31) The table below shows the soft drinks preferences of people in three age groups.
cola root beer lemon-lime
under 21 years of age 40
25
20
between 21 and 40 35
20
30
over 40 years of age 20
30
35
If one of the 255 subjects is randomly selected, find the probability that the person is over 40 years of age.
Find the indicated value.
32) z0.02
33) z0.005
Provide an appropriate response.
34) Which of the following is true about the distribution of IQ scores?
A) The standard deviation is 15.
B) The mean is 1.
C) The mean is 75.
D) The median is 10.
35) Which of the following is true about the distribution of IQ scores?
A) The area under its bell-shaped curve is 5.
B) The area under its bell-shaped curve is 10.
C) The area under its bell-shaped curve is 2.
D) The area under its bell-shaped curve is 1.
36) Find the area of the shaded region. The graph depicts IQ scores of adults, and those scores are normally
distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler test).
37) Find the indicated IQ score. The graph depicts IQ scores of adults, and those scores are normally distributed
with a mean of 100 and a standard deviation of 15 (as on the Wechsler test).
The shaded area under the curve is 0.10.
38) Find the IQ score separating the top 16% from the others.
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Assume that X has a normal distribution, and find the indicated probability.
39) The mean is µ = 15.2 and the standard deviation is = 0.9.
Find the probability that X is greater than 17.
40) The mean is µ = 22.0 and the standard deviation is = 2.4.
Find the probability that X is between 19.7 and 25.3.
41) The mean is µ = 137.0 and the standard deviation is = 5.3.
Find the probability that X is between 134.4 and 140.1.
Find the indicated probability.
42) 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?
43) The incomes of trainees at a local mill are normally distributed with a mean of $1100 and a standard deviation
of $150. What percentage of trainees earn less than $900 a month?
Solve the problem.
44) The amount of snowfall falling in a certain mountain range is normally distributed with a mean of 104 inches,
and a standard deviation of 10 inches. What is the probability that the mean annual snowfall during 25
randomly picked years will exceed 106.8 inches?
45) 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. What is the probability that the mean annual precipitation during
36 randomly picked years will be less than 109.8 inches?
46) Assume that women's heights are normally distributed with a mean of 63.6 inches and a standard deviation of
2.5 inches. If 90 women are randomly selected, find the probability that they have a mean height between 62.9
inches and 64.0 inches.
47) A study of the amount of time it takes a mechanic to rebuild the transmission for a 2005 Chevrolet Cavalier
shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics are randomly selected,
find the probability that their mean rebuild time is less than 7.6 hours.
48) A study of the amount of time it takes a mechanic to rebuild the transmission for a 2005 Chevrolet Cavalier
shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics are randomly selected,
find the probability that their mean rebuild time is less than 8.9 hours.
Find the indicated probability. Express your answer as a simplified fraction unless otherwise noted.
49) The table below shows the soft drinks preferences of people in three age groups.
cola root beer lemon-lime
under 21 years of age 40
25
20
between 21 and 40 35
20
30
over 40 years of age 20
30
35
If one of the 255 subjects is randomly selected, find the probability that the person is over 40 and drinks cola.
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50) The following table contains data from a study of two airlines which fly to Small Town, USA.
Number of flights Number of flights
which were on time
which were late
Podunk Airlines
33
6
Upstate Airlines
43
5
If one of the 87 flights is randomly selected, find the probability that the flight selected arrived on time.
Find the indicated probability. Round to the nearest thousandth.
51) A sample of 4 different calculators is randomly selected from a group containing 16 that are defective and 30
that have no defects. What is the probability that at least one of the calculators is defective?
52) In a batch of 8,000 clock radios 5% are defective. A sample of 14 clock radios is randomly selected without
replacement from the 8,000 and tested. The entire batch will be rejected if at least one of those tested is defective.
What is the probability that the entire batch will be rejected?
53) In a blood testing procedure, blood samples from 6 people are combined into one mixture. The mixture will
only test negative if all the individual samples are negative. If the probability that an individual sample tests
positive is 0.11, what is the probability that the mixture will test positive?
Solve the problem. Round results to the nearest hundredth.
54) The mean of a set of data is -3.82 and its standard deviation is 2.31. Find the z score for a value of 3.99.
55) The mean of a set of data is 359.53 and its standard deviation is 63.94. Find the z score for a value of 445.29.
Determine which score corresponds to the higher relative position.
56) Which score has a higher relative position, a score of 327.6 on a test for which x = 280 and s = 28, or a score of
22.2 on a test for which x = 20 and s = 2?
Find the indicated measure.
57) The test scores of 32 students are listed below. Find P46.
32
56
70
80
37
57
71
82
41
59
74
83
44
63
74
86
46
65
75
89
48
66
77
92
53
68
78
95
55
69
79
99
Find the percentile for the data value.
58) Data set: 122 134 126 120 128 130 120 118 125 122 126 136 118 122 124 119;
data value: 128
Solve the problem.
59) The amount of snowfall falling in a certain mountain range is normally distributed with a mean of 94 inches,
and a standard deviation of 14 inches. What is the probability that the mean annual snowfall during 49
randomly picked years will exceed 96.8 inches?
60) A study of the amount of time it takes a mechanic to rebuild the transmission for a 2005 Chevrolet Cavalier
shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics are randomly selected,
find the probability that their mean rebuild time exceeds 8.7 hours.
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61) A final exam in Math 160 has a mean of 73 with standard deviation 7.8. If 24 students are randomly selected,
find the probability that the mean of their test scores is less than 70.
Identify which of these types of sampling is used: random, stratified, systematic, cluster, convenience.
62) 49, 34, and 48 students are selected from the Sophomore, Junior, and Senior classes with 496, 348, and 481
students respectively.
63) A sample consists of every 49th student from a group of 496 students.
64) A market researcher selects 500 drivers under 30 years of age and 500 drivers over 30 years of age.
65) To avoid working late, a quality control analyst simply inspects the first 100 items produced in a day.
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