Download File - Glorybeth Becker

Chapter 18 Review Problems
1. Which of the following is NOT true concerning sampling distributions?
A. If the sample size n is large, the sampling distribution of x , drawn from a normal population, is
approximately normal.
B. The mean of the sampling distribution of
C.
p̂ is equal to the population proportion p .
The mean of the sampling distribution of the difference of two means ( x1  x2 ) is equal to the
difference of the population means ( 1   2 ).

x
D. The standard deviation of the sampling distribution of
is
, where
 is the population
n
standard deviation.
E. The standard deviation of the sampling distribution of the differences of two means (
 x 1 x 2 ) is
the sum of the respective population’s standard deviations.
2. Which of the following is true?
I. The larger the sample, the smaller the spread in the sampling distribution.
II. Provided that the population size is significantly larger than the sample size, the spread of a
sampling distribution is about the same no matter what the sample size.
III. Sampling distributions from non-normal populations are approximately normal provided n is
large.
A. II only B. III only C. I and II only D. I and III only E. I, II, and III
3. A random sample of size 16 is to be taken from a normal population having mean 100 and variance 4.
What is the 90th percentile of the distribution of x ?
A. 97.44 B. 100.08 C. 100.32 D. 100.64 E. 102.56
4. A consequence of the Central Limit Theorem is that for n sufficiently large ( n > 30), if all samples
of size n are taken, the mean of the distribution of sample means

x

x
is equal to the population mean
. Since the mean of the sampling distribution is equal to the population mean,
A. a biased estimator
B. an unbiased estimator
C. a random estimator
D. a controlled variable
x
is referred to as
E. a parameter
5. The average number of push-ups a U.S. Marine does daily is 300, with a standard deviation of 50. A
random sample of 36 Marines is selected. What is the probability of obtaining a sample mean less
than 280 push-ups?
A. 0.0082 B. 0.3446 C. 0.6554 D. 0.8767 E. 0.9918
6. Which of the following statements regarding the sampling distribution of sample means is incorrect?
A. The sampling distribution is approximately normal when the population is normal or the sample
size is large.
B. The mean of the sampling distribution is the mean of the population.
C. The standard deviation of the sampling distribution is the standard deviation of the population.
D. The sampling distribution is found by taking repeated samples of the same size from the
population of interest and computing the mean of each sample.
E. All of these are correct.
7. After repeated observations, it has been determined that the waiting time at a drive-through
window of a local bank on Friday afternoons between 12 noon and 6 pm is skewed left with a mean of
3.5 minutes and a standard deviation of 1.9 minutes. A sample of 100 customers is to be taken next
Friday. What is the probability that the mean of the sample will exceed 4 minutes?
A. .0042 B. .0396 C. .042 D. .396 E. the probability cannot be determined using a normal
curve approximation
8. An investigator anticipates that the proportion of red blossoms in his hybrid plants is .15. A random
sample of 50 of his plants indicated that 22% of the blossoms were red. The standard deviation of
the sampling distribution of the sample proportions is approximately
A. .0505
B. .0586
C. .07
D. .116
E. cannot be determined
9. The manufacturer of cold medicine claims that 60% of all adults suffer at least one cold during
every winter. What is the probability that a simple random sample of 200 adults will report that
65% or more of the subjects had at least one cold last winter?
A. .925 B. .075 C. .0625 D. .05 E. .0025
Use the following information for questions 10 and 11: A machine fills containers with juice. The mean amount of juice is 48
fluid ounces per container and the standard deviation is 0.1 fluid ounces.
10. A quality control engineer takes daily samples of size 10 from the production line and computes the sample means. What is
the mean value of the distribution of sample means?
11. A quality control engineer takes daily samples of size 15 from the production line and computes the sample means. What is
the standard deviation of the distribution of sample means?
12. A consumer organization wants to test a manufacturer’s claim that its light bulbs last an average of 200 days with a standard
deviation of 20. What is the probability that the mean lifetime of a sample of 50 such bulbs is less than 195 days?
13. A mechanical press is used to mold shapes for plastic toys. When the machine is adjusted and working well, it still produces
6% defective toys. A sample of 200 toys has 7% defective toys. What is the probability of obtaining a sample with at least
7% defective?
14. The daily wages of workers in a particular industry are normally distributed with a mean of $97 and a standard deviation of
$13.20. If a random sample of size 16 is taken, what is the probability that the mean daily wage of the workers in the sample
will be less than $92?
Mixed set: Chapter 8 and Challenge Problems
1. It is known that 60% of the students in a certain college pay for their own lunch with a meal ticket rather than with cash. If
40 students in the cafeteria are sampled, what is the probability that at least 20 of them pay for their lunch with a meal
ticket?
2. The electric light bulbs of manufacturer A have a mean lifetime of 1400 hours with a standard deviation of 200 hours, while
those of manufacturer B have a mean lifetime of 1200 hours with a standard deviation of 100 hours. If random samples of 125 of
each brand are tested, what is the probability that the brand A bulbs have a mean lifetime that is at least 160 hours more than
the brand B bulbs?
3. Two machines are designed to fill cereal boxes. The mean weight of the boxes from machine A is 15.98 ounces with a
standard deviation of 0.21 ounces. The mean weight of the boxes from machine B is 16.03 ounces with a standard deviation of
0.25 ounces. Each day 100 boxes are selected at random from each production line. What is the probability that the difference
in the mean weights is less than 0.03 ounces?
Chapter 18 Review Problems
1. Which of the following is NOT true concerning sampling distributions?
A. If the sample size n is large, the sampling distribution of x , drawn from a normal population, is
approximately normal.
B. The mean of the sampling distribution of
C.
p̂ is equal to the population proportion p .
The mean of the sampling distribution of the difference of two means ( x1  x2 ) is equal to the
difference of the population means ( 1   2 ).

x
D. The standard deviation of the sampling distribution of
is
, where
 is the population
n
standard deviation.
E. The standard deviation of the sampling distribution of the differences of two means (
 x 1 x 2 ) is
the sum of the respective population’s standard deviations.
2. Which of the following is true?
I. The larger the sample, the smaller the spread in the sampling distribution.
II. Provided that the population size is significantly larger than the sample size, the spread of a
sampling distribution is about the same no matter what the sample size.
III. Sampling distributions from non-normal populations are approximately normal provided n is
large.
A. II only B. III only C. I and II only
D. I and III only E. I, II, and III
3. A random sample of size 16 is to be taken from a normal population having mean 100 and variance 4.
What is the 90th percentile of the distribution of x ?
A. 97.44 B. 100.08 C. 100.32 D. 100.64 E. 102.56
4. A consequence of the Central Limit Theorem is that for n sufficiently large ( n > 30), if all samples
of size n are taken, the mean of the distribution of sample means

x

x
is equal to the population mean
. Since the mean of the sampling distribution is equal to the population mean,
A. a biased estimator
B. an unbiased estimator
C. a random estimator
D. a controlled variable
x
is referred to as
E. a parameter
5. The average number of push-ups a U.S. Marine does daily is 300, with a standard deviation of 50. A
random sample of 36 Marines is selected. What is the probability of obtaining a sample mean less
than 280 push-ups?
A. 0.0082 B. 0.3446 C. 0.6554 D. 0.8767
E. 0.9918
6. Which of the following statements regarding the sampling distribution of sample means is incorrect?
A. The sampling distribution is approximately normal when the population is normal or the sample
size is large.
B. The mean of the sampling distribution is the mean of the population.
C. The standard deviation of the sampling distribution is the standard deviation of the population.
D. The sampling distribution is found by taking repeated samples of the same size from the
population of interest and computing the mean of each sample.
E. All of these are correct.
7. After repeated observations, it has been determined that the waiting time at a drive-through
window of a local bank on Friday afternoons between 12 noon and 6 pm is skewed left with a mean of
3.5 minutes and a standard deviation of 1.9 minutes. A sample of 100 customers is to be taken next
Friday. What is the probability that the mean of the sample will exceed 4 minutes?
A. .0042 B. .0396 C. .042 D. .396 E. the probability cannot be determined using a normal
curve approximation
8. An investigator anticipates that the proportion of red blossoms in his hybrid plans is .15. A random
sample of 50 of his plans indicated that 22% of the blossoms were red. The standard deviation of
the sampling distribution of the sample proportions is approximately
A. .0505
B. .0586
C. .07
D. .116
E. cannot be determined
9. The manufacturer of cold medicine claims that 60% of all adults suffer at least one cold during
every winter. What is the probability that a simple random sample of 200 adults will report that
65% or more of the subjects had at least one cold last winter?
A. .925 B. .075 C. .0625 D. .05 E. .0025
Use the following information for questions 10 and 11: A machine fills containers with juice. The mean amount of juice is 48
fluid ounces per container and the standard deviation is 0.1 fluid ounces.
10. A quality control engineer takes daily samples of size 10 from the production line and computes the sample means. What is
the mean value of the distribution of sample means? 48
11. A quality control engineer takes daily samples of size 15 from the production line and computes the sample means. What is
the standard deviation of the distribution of sample means?
.0258
12. A consumer organization wants to test a manufacturer’s claim that its light bulbs last an average of 200 days with a standard
deviation of 20. What is the probability that the mean lifetime of a sample of 50 such bulbs is less than 195 days?
.0385
13. A mechanical press is used to mold shapes for plastic toys. When the machine is adjusted and working well, it still produces
6% defective toys. A sample of 200 toys has 7% defective toys. What is the probability of obtaining a sample with at least
7% defective?
.2758
14. The daily wages of workers in a particular industry are normally distributed with a mean of $97 and a standard deviation of
$13.20. If a random sample of size 16 is taken, what is the probability that the mean daily wage of the workers in the sample
will be less than $92?
.0649
Mixed set: Chapter 8 and Challenge Problems
1. It is known that 60% of the students in a certain college pay for their own lunch with a meal ticket rather than with cash. If
40 students in the cafeteria are sampled, what is the probability that at least 20 of them pay for their lunch with a meal
ticket?
Binomial: .9256; Normal: .9016
2. The electric light bulbs of manufacturer A have a mean lifetime of 1400 hours with a standard deviation of 200 hours, while
those of manufacturer B have a mean lifetime of 1200 hours with a standard deviation of 100 hours. If random samples of 125 of
each brand are tested, what is the probability that the brand A bulbs have a mean lifetime that is at least 160 hours more than
the brand B bulbs?
.9772
3. Two machines are designed to fill cereal boxes. The mean weight of the boxes from machine A is 15.98 ounces with a
standard deviation of 0.21 ounces. The mean weight of the boxes from machine B is 16.03 ounces with a standard deviation of
0.25 ounces. Each day 100 boxes are selected at random from each production line. What is the probability that the difference
in the mean weights is less than 0.03 ounces?
.2629
KEY:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
E
D
D
B
A
C
A
A
B
48
.0258
.0385
.2758
.0649
Mixed Set:
1.
2.
3.
Binomial: .9256; Normal: .9016
.9772
.2629