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Study Guide
Chapters 5 and 6
1)
Assume that men gave heights that are normally distributed with a mean of 68 in. and a
standard deviation of 2.8 in. Find the height for the given percentile
a)
P40
b)
P88
2)
Replacement times for CD players are normally distributed with a mean of 7.1 years and a
standard deviation of 1.4 years. Find the replacement time separating the top 45% from the bottom
55%.
3)
The serum cholesterol levels in men aged 18 to 24 years are normally distributed with a
mean of 178.1 and a standard deviation of 40.7.
a)
If a man aged 18 to 24 is randomly selected, find the probability that his serum
cholesterol level is less than 200.
Elliott
b)
If a serum cholesterol level is deemed to be too high if it is in the top 7%, find the
cutoff level for readings that are too high.
c)
If 45 men are selected, find the probability that their mean cholesterol level is
between 177 and 200.
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4)
Suppose that replacement times for refrigerators are normally distributed with a mean
of 8.7 years and a standard deviation of 1.5 years. Find the replacement time that separates the
top 27% from the bottom 73%.
A study was made of seat-belt use among children who were involved in car crashes that
5)
caused then to be hospitalized. It was found that children not wearing any restraints had hospital
stays with a mean of 7.37 days and a standard deviation of 0.79 day. If 40 such children are
randomly selected, find the probability that their mean hospital stay is greater than 7.00 days.
6) Find a 92% confidence interval for the population mean where x = 34.5 , n = 36, and σ = 2.8 .
7) Find a 95% confidence interval for the population mean where n = 12, x = 20 , and s = 2.5.
Assume bell-shaped.
8) A company must adjust its vending machines to accept only coins with specified weights. We
will obtain a sample of quarters and weigh them to determine the mean. How many quarters must
we randomly select and weigh if we want to be 99% confident that the sample mean is within 0.025
g of the true population mean for all quarters? Assume that the population standard deviation is
0.068 g.
Elliott
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9) The tobacco industry closely monitors all surveys that involve smoking. One survey showed
that among 785 randomly selected subjects who completed 4 years of college, 18.3% smoke.
Construct the 90% confidence interval for the true percentage of smokers among all people who
completed 4 years of college.
10) Find the critical values for the following situation(s):
a) You wish to construct a 92% confidence interval estimate of the population mean with
the following sample data. A sample size of 126 gave a sample mean of 34.5 with a
standard deviation of 2.5.
b) A sample was taken of the heights of women in the Tlingit village of Ketchikan. 24
women were sampled, and a mean height of 59 inches with a standard deviation of 3.4
inches was found. Find the critical values only, if a 98% confidence interval estimate
was constructed for the mean height of all Tlingit women.
11)
A random sample of 10 parking meters in a beach community showed the following
incomes for a day. Assume the incomes are normally distributed.
$3.60
$8.00
$4.50
$3.00
$2.80
$6.30
$2.60
$5.20
$6.75
$4.25
Find the 95% confidence interval for the true mean for this data.
12)
A researcher at a major hospital wishes to estimate the proportion of the adult population of
the United States that has high blood pressure. How large a sample is needed in order to be
99% confident that the sample proportion will not differ from the true proportion by more
than 3%?
13)
The grade point averages for 25 randomly selected students in a statistics class are found and
a confidence interval is created. What would be the effect on the width of the confidence
interval if the standard deviation is increased? (Circle one)
A. The width increases.
B. The width decreases
C. The width remains the same.
D. It is impossible to tell from
this information.
Elliott
Spring’11