For samples of the specified size from the population described, find the mean and standard deviation of the sample
mean x.
38)
The mean and the standard deviation of the sampled population are, respectively, 125.4 and 24.1.
n =49
38)
A)
µx
=125.4;
x
=3.4
B)
µx
=201.5;
x
=1.3
C)
µx
=24.1;
x
=3.4
D)
µx
=3.4;
x
=125.4
Find the requested probability.
39)
The test scores of 5 students are under consideration. The following is the dotplot for the sampling
distribution of the sample mean for samples of size 2.
Find the probability, expressed as a percent, that the sample mean will be within 1 point of the
population mean.
39)
A)
25%
B)
20%
C)
10%
D)
30%
40)
The test scores of 5 students are under consideration. The following is the dotplot for the sampling
distribution of the sample mean for samples of size 2.
Find the probability, expressed as a percent, that the sample mean will be within 3 points of the
population mean.
40)
A)
50%
B)
72%
C)
40%
D)
60%
For samples of the specified size from the population described, find the mean and standard deviation of the sample
mean x.
41)
The National Weather Service keeps records of snowfall in mountain ranges. Records indicate that
in a certain range, the annual snowfall has a mean of 82 inches and a standard deviation of 12
inches. Suppose the snowfalls are sampled during randomly picked years. For samples of size 36,
determine the mean and standard deviation of x.
41)
A)
µx
=12;
x
=82
B)
µx
=2;
x
=82
C)
µx
=82;
x
=2
D)
µx
=82;
x
=12
Find the indicated probability or percentage for the sampling error.
42)
The monthly expenditures on food by single adults in one city are normally distributed with a
mean of $410 and a standard deviation of $70. What is the probability that the sampling error made
in estimating the mean monthly expenditure of all single adults in that city by the mean of a
random sample of 90 such adults will be at most $10?
42)
A)
0.9990
B)
0.1114
C)
0.8262
D)
0.9131
Provide an appropriate response.
43)
The mean height for a population is 65 inches and the standard deviation is 3 inches. Let A and B
denote the events described below.
Event A: The mean height in a random sample of 16 people is within 1 inch of the population
mean.
Event B: The mean height in a random sample of 50 people is within 1 inch of the population
mean.
True or false, the probability of event A is greater than the probability of event B?
43)
A)
True
B)
False
Find the indicated probability or percentage for the sampling error.
44)
The amount of coffee that a filling machine puts into an 8–ounce jar is normally distributed with a
mean of 8.2 ounces and a standard deviation of 0.18 ounce. Determine the percentage of samples of
size 16 that will have mean amounts of coffee within 0.1 ounce of the population mean of 8.2
ounces.
44)
A)
42.46%
B)
98.68%
C)
71.23%
D)
97.36%
Identify the distribution of the sample mean. In particular, state whether the distribution of x is normal or approximately
normal and give its mean and standard deviation.
45)
The heights of people in a certain population are normally distributed with a mean of 64 inches and
a standard deviation of 3.7 inches. Determine the sampling distribution of the mean for samples of
size 40.
45)
A)
Approximately normal, mean =64 inches, standard deviation =0.09 inches
B)
Normal, mean =64 inches, standard deviation =3.7 inches
C)
Normal, mean =64 inches, standard deviation =0.09 inches
D)
Normal, mean =64 inches, standard deviation =0.59 inches
For samples of the specified size from the population described, find the mean and standard deviation of the sample
mean x.
46)
The mean and the standard deviation of the sampled population are, respectively, 75.8 and 8.9.
n =361
46)
A)
µx
=45.0;
x
=2.2
B)
µx
=0.5;
x
=75.8
C)
µx
=8.9;
x
=0.5
D)
µx
=75.8;
x
=0.5
Find the indicated probability or percentage for the sampling error.
47)
The monthly expenditures on food by single adults living in one neighborhood of Los Angeles are
normally distributed with a mean of $370 and a standard deviation of $100. Determine the
percentage of samples of size 25 that will have mean monthly expenditures on food within $36 of
the population mean expenditure of $370.
47)
A)
63.18%
B)
92.82%
C)
96.41%
D)
46.41%
20
48)
The distribution of weekly salaries at a large company is reverse J–shaped with a mean of $1000
and a standard deviation of $370. What is the probability that the sampling error made in
estimating the mean weekly salary for all employees of the company by the mean of a random
sample of weekly salaries of 80 employees will be at most $75?
48)
A)
0.9298
B)
0.0702
C)
0.4649
D)
Cannot be determined, because the distribution of the population is not normal.
Provide an appropriate response.
49)
The mean height for a population is 65 inches and the standard deviation is 3 inches. Let A and B
denote the events described below.
Event A: The height of a randomly selected person is 5 inches or more from the population mean.
Event B: The mean height in a random sample of 16 people is 5 inches or more from the population
mean.
True or false, the probability of event A is greater than the probability of event B?
49)
A)
True
B)
False
50)
As a general rule, you cannot expect to exactly determine the sampling distribution of a statistic.
Why?
50)
A)
Many populations are too large.
B)
Many populations are not uniform.
C)
Many populations are too small.
D)
Many populations are not normal.
Find the indicated probability or percentage for the sampling error.
51)
The distribution of weekly salaries at a large company is right skewed with a mean of $1000 and a
standard deviation of $350. What is the probability that the sampling error made in estimating the
mean weekly salary for all employees of the company by the mean of a random sample of weekly
salaries of 50 employees will be at most $50?
51)
A)
0.3124
B)
0.3438
C)
0.6876
D)
Cannot be determined, because the distribution of the population is not normal.
Provide an appropriate response.
52)
What is the sampling distribution of a statistic?
52)
A)
The distribution of all possible observations of the statistic for samples of a given size from a
population
B)
The distribution of observations of a variable in a sample for a given value of the statistic
C)
The distribution of all possible sizes of samples from a population that can be used to make
observations of the statistic
D)
The distribution of observations of the statistic for all possible sizes of samples from a
population
53)
What generally happens to the sampling error as the sample size is decreased?
53)
A)
It gets more predictable.
B)
It gets smaller.
C)
It gets less predictable.
D)
It gets larger.
54)
The mean height for a population is 65 inches. Let x denote the mean height for a sample of people
picked randomly from the population. True or false, the standard deviation of x for samples of size
30 is smaller than the standard deviation, , of the population?
54)
A)
True
B)
False
55)
The mean height for a population is 65 inches and the standard deviation is 3 inches. Let A and B
denote the events described below.
Event A: The height of a randomly selected person is within 3 inches of the population mean.
Event B: The mean height in a random sample of 16 people is within 3 inches of the population
mean.
True or false, the probability of event A is greater than the probability of event B?
55)
A)
True
B)
False
Find the requested probability.
56)
The test scores of 5 students are under consideration. The following is the dotplot for the sampling
distribution of the sample mean for samples of size 2.
Find the probability, expressed as a percent, that the sample mean will be within 2 points of the
population mean.
56)
A)
50%
B)
60%
C)
30%
D)
40%
Find the indicated probability or percentage for the sampling error.
57)
The amount of coffee that a filling machine puts into an 8–ounce jar is normally distributed with a
mean of 8.2 ounces and a standard deviation of 0.18 ounce. What is the probability that the
sampling error made in estimating the mean amount of coffee for all 8–ounce jars by the mean of a
random sample of 100 jars will be at most 0.02 ounce?
57)
A)
0.7330
B)
0.0938
C)
0.0876
D)
0.8665
Provide an appropriate response.
58)
How many different samples of size 2 can be obtained from a population of size 5?
58)
A)
1
B)
2
C)
10
D)
5
Find the requested probability.
59)
The test scores of 5 students are under consideration. The following is the dotplot for the sampling
distribution of the sample mean for samples of size 2.
Find the probability, expressed as a percent, that the sample mean will be within 3 points of the
population mean.
59)
A)
50%
B)
60%
C)
70%
D)
40%
Identify the distribution of the sample mean. In particular, state whether the distribution of x is normal or approximately
normal and give its mean and standard deviation.
60)
The mean annual income for adult women in one city is $28,520 and the standard deviation of the
incomes is $5100. The distribution of incomes is skewed to the right. Determine the sampling
distribution of the mean for samples of size 71.
60)
A)
Normal, mean = $28,520, standard deviation = $72
B)
Approximately normal, mean = $28,520, standard deviation = $605
C)
Normal, mean = $28,520, standard deviation = $605
D)
Approximately normal, mean = $28,520, standard deviation = $5100
Find the requested probability.
61)
The table reports the GPA for each of five students in a statistics class.
Student Maria Alvin Elvis Ingrid Rashad
GPA 3.52 3.65 3.66 3.92 3.95
For a random sample of size two, find the probability, expressed as a percent, that the sample mean
will be within 0.1 of the population mean.
61)
A)
30%
B)
80%
C)
70%
D)
20%
62)
The test scores of 5 students are under consideration. The following is the dotplot for the sampling
distribution of the sample mean for samples of size 2.
Find the probability, expressed as a percent, that the sample mean will be equal to the population
mean.
62)
A)
5%
B)
30%
C)
10%
D)
20%
Identify the distribution of the sample mean. In particular, state whether the distribution of x is normal or approximately
normal and give its mean and standard deviation.
63)
The weights of people in a certain population are normally distributed with a mean of 154 lb and a
standard deviation of 23 lb. Determine the sampling distribution of the mean for samples of size 4.
63)
A)
Approximately normal, mean =154 lb, standard deviation =11.5 lb
B)
Approximately normal, mean =154 lb, standard deviation =5.75 lb
C)
Normal, mean =154 lb, standard deviation =23 lb
D)
Normal, mean =154 lb, standard deviation =11.5 lb
Provide an appropriate response.
64)
What generally happens to the sampling distribution of the sample mean as the sample size is
decreased?
64)
A)
It is unaffected.
B)
It becomes less tightly concentrated around the population mean.
C)
It becomes more tightly concentrated around the population mean.
D)
None of the above
Find the requested probability.
65)
The test scores of 5 students are under consideration. The following is the dotplot for the sampling
distribution of the sample mean for samples of size 2.
Find the probability, expressed as a percent, that the sample mean will be within 1 point of the
population mean.
65)
A)
5%
B)
22%
C)
20%
D)
10%
66)
The test scores of 5 students are under consideration. The following is the dotplot for the sampling
distribution of the sample mean for samples of size 2.
Find the probability, expressed as a percent, that the sample mean will be within 5 points of the
population mean.
66)
A)
100%
B)
95%
C)
80%
D)
90%
67)
The test scores of 5 students are under consideration. The following is the dotplot for the sampling
distribution of the sample mean for samples of size 2.
Find the probability, expressed as a percent, that the sample mean will be within 2 points of the
population mean.
67)
A)
30%
B)
40%
C)
20%
D)
50%
Identify the distribution of the sample mean. In particular, state whether the distribution of x is normal or approximately
normal and give its mean and standard deviation.
68)
For the population of one town, the number of siblings, x, is a random variable whose relative
frequency histogram has a reverse J–shape. The mean number of siblings is 1.3 and the standard
deviation is 1.5. Let x denote the mean number of siblings for a random sample of size 35.
Determine the sampling distribution of the mean for samples of size 35.
68)
A)
Normal, mean =1.3, standard deviation =1.5
B)
Approximately normal, mean =1.3, standard deviation =0.25
C)
Approximately normal, mean =1.3, standard deviation =1.5
D)
Normal, mean =1.3, standard deviation =0.25
For samples of the specified size from the population described, find the mean and standard deviation of the sample
mean x.
69)
One truck from Lakeland Trucking, Inc. can carry a load of 2959.2 lb. Records show that the
weights of boxes that it carries have a mean of 78 lb and a standard deviation of 12 lb. For samples
of size 36, find the mean and standard deviation of x.
69)
A)
µx
=78;
x
=2
B)
µx
=2;
x
=78
C)
µx
=12;
x
=78
D)
µx
=78;
x
=12
Provide an appropriate response.
70)
The mean height for a population is 65 inches and the standard deviation is 3 inches. Let x denote
the mean height for a sample of people picked randomly from the population. True or false, the
standard deviation of x for samples of size 30 is greater than the standard deviation of x for
samples of size 20?
70)
A)
True
B)
False
Identify the distribution of the sample mean. In particular, state whether the distribution of x is normal or approximately
normal and give its mean and standard deviation.
71)
Let x represent the number that shows up when a balanced die is rolled. Then x is a random
variable with a mean of 3.5 and a standard deviation of 1.71. Let x denote the mean of the numbers
obtained when the die is rolled 34 times. Determine the sampling distribution of x.
71)
A)
Approximately normal, mean = 3.5, standard deviation =0.29
B)
Normal, mean = 3.5, standard deviation =0.05
C)
Approximately normal, mean = 3.5, standard deviation = 1.71
D)
Normal, mean = 3.5, standard deviation =0.29
Find the indicated probability or percentage for the sampling error.
72)
The monthly expenditures on food by single adults living in one neighborhood of Los Angeles are
normally distributed with a mean of $410 and a standard deviation of $75. Determine the
percentage of samples of size 9 that will have mean monthly expenditures on food within $20 of
the population mean expenditure of $410.
72)
A)
57.62%
B)
91.92%
C)
21.28%
D)
98.36%
Find the requested probability.
73)
The table reports the distribution of pocket money, in bills, of the 6 students in a statistics seminar.
Student Hannah Ming Keshaun Tameeka Jose Vaishali
Amount, in dollars 2 4 4 5 5 7
For a random sample of size two, find the probability, expressed as a percent rounded to the
nearest tenth, that the sample mean will be within $1 of the population mean.
73)
A)
78.6%
B)
66.7%
C)
73.3%
D)
80.0%
Find the indicated probability or percentage for the sampling error.
74)
Scores on an aptitude test are distributed with a mean of 220 and a standard deviation of 30. The
shape of the distribution is unspecified. What is the probability that the sampling error made in
estimating the population mean by the mean of a random sample of 50 test scores will be at most
5 points?
74)
A)
0.881
B)
0.135
C)
0.762
D)
Cannot be determined, because the distribution of the population is not known to be normal.
For samples of the specified size from the population described, find the mean and standard deviation of the sample
mean x.
75)
One barge from Inland Waterways, Inc. can carry a load of 2655 lb. Records of past trips show that
the weights of the cans that it carries have a mean of 102 lb and a standard deviation of 10 lb. For
samples of size 25, find the mean and standard deviation of x.
75)
A)
µx
=102;
x
=2
B)
µx
=102;
x
=10
C)
µx
=2;
x
=102
D)
µx
=10;
x
=102
76)
The National Weather Service keeps records of rainfall in valleys. Records indicate that in a certain
valley, the annual rainfall has a mean of 84 inches and a standard deviation of 14 inches. Suppose
the rainfalls are sampled during randomly picked years and x is the mean amount of rain in these
years. For samples of size 49, determine the mean and standard deviation of x.
76)
A)
µx
=2;
x
=84
B)
µx
=84;
x
=14
C)
µx
=14;
x
=84
D)
µx
=84;
x
=2
Answer Key
Testname: C7
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Answer Key
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Answer Key
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Answer Key
Testname: C7
Answer Key
Testname: C7