Review
1. Calculate the mean for the discrete probability distribution shown here.
X
P(X)
2
.2
4
.2
5
.3
10
.2
2. It has been stated that 20% of the general population donate their time and
energy to working on community projects. Suppose 20 people have been
randomly sampled from a community and asked if they donated their time and
energy to community projects. Let x be the number of them that do donate their
time and energy to community projects. Find the probability that more than
seven of the 20 do donate their time and energy to community projects.
3. A firm believes the internal rate of return for its proposed investment can best
be described by a normal distribution with mean 20% and standard deviation
3%. What is the probability that the internal rate of return for the investment
will be at least 15.5%?
4. The board of examiners that administers the real estate broker's examination in
a certain state found that the mean score on the test was 435 and the standard
deviation was 72. If the board wants to set the passing score so that only the
best 10% of all applicants pass, what is the passing score? Assume that the
scores are normally distributed.
5. The tread life of a particular brand of tire is a random variable best described by
a normal distribution with a mean of 60,000 miles and a standard deviation of
8,300 miles. If the manufacturer guarantees the tread life of the tires for the first
50,000 miles, what proportion of the tires will need to be replaced under
warranty?
6. The amount of money collected by the snack bar at a large university has been
recorded daily for the past five years. Records indicate that the mean daily
amount collected is $2,500 and the standard deviation is $400. The distribution
is skewed to the right due to several high volume days (football game days).
Suppose that 100 days were randomly selected from the five years and the
average amount collected from those days was recorded. Describe the sampling
distribution of the sample mean?
7. The scores shot by professional golfers on a particular course have a mean of 70
strokes and a standard deviation of three strokes. Suppose 40 professional
golfers played the course today. Find the approximate probability that the
average score for the 40 golfers was below 72.
8. Electric power plants that use water for cooling their condensers sometimes
discharge heated water into rivers, lakes, or oceans. It is known that water
heated above certain temperatures has a detrimental effect on the plant and
animal life in the water. Suppose it is known that the increased temperature of
the heated water discharged by a certain power plant on any given day has a
distribution with a mean of 50C and a standard deviation of 50C. Suppose a
sample of n = 50 days was collected. What is the approximate probability that
the average increase in temperature of the discharged water exceeds 6 0C.
9. The length of time to complete a door assembly on an automobile factory
assembly line is distributed with mean µ = 7.0 minutes and standard deviation
 = 5.0 minutes. What is the probability that the mean assembly time for a
random sample of 100 doors will be:
o At least 6 minutes
o 8 minutes or less
o Between 6.0 and 6.5 minutes
o Between 4.5 and 8 minutes
10. A physician wanted to estimate the mean length of time  that a patient had to
wait to see him after arriving at the office. A random sample of 36 patients showed
a mean waiting time of 23.4 minutes and a standard deviation of 7.2 minutes. Find
a 96% confidence interval for  .
11. Barbara wanted to estimate the mean connection time  to the Internet. She
connected 25 times with a mean of 42 and a standard deviation of 5.2 minutes.
Find a 90% confidence interval for  .
12. A sample of 121 calls to the 900 number you operate has a mean duration of
16.6 minutes and a standard deviation of 3.63 minutes. You offer a discount,
which will be discontinued unless the mean call duration exceeds 18 minutes. At
the 90 percent level of confidence, what is your decision? Based on this study, do
you think the service discount should be discontinued?
13. To estimate the proportion p of passengers who had purchased tickets for more
than $400 over a year's time, an airline official obtained a random sample of 75.
The number of those purchasing tickets for more than $400 was 45.
(a) What is a point estimate for p?
(b) Find a 90% confidence interval for p.
(c) How many passengers are required in the sample to reduce in half the
sampling error within which we need to estimate the proportion of passengers
who had purchased tickets for more than $400 over a year's time?
14. A city council commissioned a statistician to estimate the proportion p of voters
in favor of a proposal to build a new library. The statistician obtained a random
sample of 200 voters, with 112 indicating approval of the proposal. What is a
point estimate for p? Find a 99% confidence interval for p.
15. A coin is tossed 1000 times and 540 heads appear. Find a 95% confidence
interval for the true proportion of heads.
16. A marketing research company is estimating the average total compensation of
CEOs in the service industry. Data were randomly collected from 18 CEOs and
the 90% confidence interval was calculated to be
Give a
practical interpretation of the confidence interval.
17. If you wish to estimate a population mean within 0.2 using a 98% confidence
interval and you know from prior sampling of sample size n = 500 that s is equal
to 5.0. How many more observations would you have to include in your sample?
18. Allen is an appliance salesman who works on commission. A random sample of
49 days showed that the sample standard deviation for value of sales was S =
$202. How many days must be included in the sample to be 99% sure the
population mean μ is within $45 of the sample mean X-bar?
19. A nurse at a local hospital is interested in estimating the birth weight of
infants. How large a sample must she select if she desires to be 90%
confident that the true mean is within 2 ounces of the sample mean? The
standard deviation of the birth weights is known to be 10 ounces.