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Probability and Statistics
Review: Topics in Chapters 5-7
Name ______________________
Solve the following problems using the concepts in chapters 5-7. Show all
work!!!
1. Phone bills for residents of Cincinnati are normally distributed and
have a mean of $64 and a standard deviation of $9. Random samples
of 36 phone bills are drawn from this population and the mean of each
sample is determined. Find the mean and standard error of the mean
of the sampling distribution.
2. The values below represent the arm lengths (in centimeters) of male
machine operators. Construct the 90% confidence interval for the
mean arm length.
76.8
70.9
75.6
71.7
69.3
69.4
75.7
72.5
75.5
72.2
71.2
68.5
72.5
75.9
71.9
73.0
3. In a random sample of 15 CD players brought in for repair, the
average repair cost was $80 and the standard deviation was $14.
Assuming that the repair costs are normally distributed, construct a
95% confidence interval for the population mean. Explain what this
interval represents. Would a 98% confidence interval be larger or
smaller? Why? (Decide without actually constructing the confidence
interval)
4. The average sales price of an existing single-family house in the
United States is $175,700. You randomly select 16 single-family
houses. What is the probability that the mean sales price is more
than $170,000? Assume that the sales prices are normally
distributed with a standard deviation of $26,000.
5. During a certain week the mean price of gasoline in the New England
region was  = $1.080 per gallon. What is the probability that the
mean price for a sample of 32 randomly selected gas stations in that
area was between $1.075 and $1.090 that week. Assume that  =
$0.045.
6. A college admissions director wishes to estimate the mean age of all
students currently enrolled. In a random sample of 35 students, the
mean age is found to be 22.9 years. From past studies, the standard
deviation is known 1.5 years. Construct a 90% confidence interval of
the population mean age.
7. Prices for sound-system receivers are normally distributed, with a
mean price of $625 and a standard deviation of $150.
a. What is the probability that a randomly selected receiver costs
less than $700?
b. You randomly select 10 receivers. What is the probability that
their mean cost is less than $700? Why are you able to do this
problem even though the sample size is less than 30?
8. In crash tests of 15 minivans, collision repair costs are found to have
a distribution that is roughly bell-shaped with a mean of $1786 and a
standard deviation of $937. Construct the 99% confidence interval
for the mean repair cost in all such vehicle collisions.