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TEST 2 on chapters 5, 6, 7
NAME____________________
Math 12 Statistics Venable Fall 2008
Please show all work for partial credit. Use separate paper if you need more room.
1) The mean annual water bill for all households in a community is $480. Assume that the annual
water bills for all households in the community follow a normal distribution with mean $480 and
standard deviation $100. The city planner is interested in houses that spend more that $600 per
year. What is the probability that a randomly selected household from the community falls into
this category?
2) A continuous random variable x produces a right-skewed distribution with a mean of 78 and a
standard deviation of 8. Calculate the mean and standard deviation of the sampling distribution of
the sample mean for a sample of 16 elements taken from this population.
a) Will this sampling distribution be normal?
b) Why or why not?
c) What could be done to make the shape of the sampling distribution normal?
3) Sixteen percent of adults contribute to charitable agencies on a regular basis. Using the binomial
formula, find the probability that in a random sample of twelve adults, exactly five contribute to
charitable agencies on a regular basis.
Page 1 of 5
4) The following table gives the frequency distribution of the number of suits owned by all 130
managers of all companies in a city.
Number of Suits
3
4
5
6
7
8
Number of Managers
15
21
31
28
26
9
a) Construct the probability distribution table for the number of suits owned by managers of these
130 companies.
x
P(x)
b) Let x denote the number of suits owned by a manager selected at random from these companies.
Find the probability that P(x > 5).
5) Suppose a certain brand of calculator has a mean life of 70 months with a standard deviation
of 8 months. The manufacturer wants to offer a warrantee on these calculators, but does not
want to replace more that 5% of the calculators under the warrantee. What should the
manufacturer choose as the length of the warrantee period under these conditions?
Page 2 of 5
6) Seventy percent of adults are in favor of reducing defense expenditure and spending the same
money on education and health care. Using the binomial probabilities table, find the probability
that in a random sample of eight adults, at least five will be in favor of reducing defense
expenditure and spending the same money on education and health care.
7) We know that 20% of all families own stocks. A random sample of 600 families is taken. Find the
probability that 125 or more in the sample own stocks.
8) The editor of a journal historically accepts twelve percent of articles submitted for publication.
Using the binomial formula, find the probability that in a random sample of twenty articles
submitted to this journal, the editor will accept exactly three for publication.
Page 3 of 5
9) The following data give the years of schooling for all four employees of a company.
16
12
14
16
a) Calculate the population mean.
b) Take all possible samples of size 3 without replacement. Calculate the sample mean and the
sampling error for each sample.
c) Show that x̄ =  in this example.
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10) All five employees of a company were asked if they are smokers or nonsmokers. The following
data give the information on these employees.
smoker
nonsmoker nonsmoker
smoker
nonsmoker
a) Calculate p, the proportion of employees of this company that are nonsmoker.
b) Take all possible samples of size 3 that you can take from this population and calculate the
sample proportion and the sampling error for each sample.
c) Show that  p^ = p in this example.
Page 5 of 5