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# Hypergeometric, binomial and uniform distribution

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1.The Internal Revenue Service is studying the category of charitable contributions. A sample of 20 returns is selected from young couples between the ages of 20 and 35 who had an adjusted gross income of more than \$100,000. Of these 20 returns, 6 had charitable contributions of more than \$1,000. Suppose 4 of these returns are selected for a comprehensive audit.

a You should use the hypergeometric distribution is appropriate. Because

b. What is the probability exactly one of the four audited had a charitable deduction of more than \$1,000? (Round your answer to 4 decimal places.)

Probability

c.What is the probability at least one of the audited returns had a charitable contribution of more than \$1,000? (Round your answer to 4 decimal places.)

Probability

2. The director of admissions at Kinzua University in Nova Scotia estimated the distribution of student admissions for the fall semester on the basis of past experience.

1,040 0.5
1,400 0.2
1,580 0.3

1. What is the expected number of admissions for the fall semester?

2.Compute the variance and the standard deviation of the number of admissions. (Round your standard deviation to 2 decimal places.)

Variance

Standard deviation

According to the "January theory," if the stock market is up for the month of January, it will be up for the year. If it is down in January, it will be down for the year. According to an article in The Wall Street Journal, this theory held for 28 out of the last 34 years. Suppose there is no truth to this theory; that is, the probability it is either up or down is 0.5.

What is the probability this could occur by chance? (Round your answer to 6 decimal places.)

Probability

3. According to the "January theory," if the stock market is up for the month of January, it will be up for the year. If it is down in January, it will be down for the year. According to an article in The Wall Street Journal, this theory held for 28 out of the last 34 years. Suppose there is no truth to this theory; that is, the probability it is either up or down is 0.5.

What is the probability this could occur by chance? (Round your answer to 6 decimal places.)

Probability

4. Customers experiencing technical difficulty with their internet cable hookup may call an 800 number for technical support. It takes the technician between 150 seconds and 15 minutes to resolve the problem. The distribution of this support time follows the uniform distribution.

a.What are the values for a and b in minutes? (Do not round your intermediate calculations. Round your answers to 1 decimal place.)

a

b

b-1. What is the mean time to resolve the problem? (Do not round your intermediate calculations. Round your answer to 2 decimal places.)

Mean

b-2. What is the standard deviation of the time? (Do not round your intermediate calculations. Round your answer to 2 decimal places.)

Standard deviation

c.What percent of the problems take more than 5 minutes to resolve? (Do not round your intermediate calculations. Round your answer to 2 decimal places.)

Percent
%

d.Suppose we wish to find the middle 50% of the problem-solving times. What are the end points of these two times? (Do not round your intermediate calculations. Round your answers to 3 decimal places.)

End point 1

End point 2

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#### Solution Preview

1.The Internal Revenue Service is studying the category of charitable contributions. A sample of 20 returns is selected from young couples between the ages of 20 and 35 who had an adjusted gross income of more than \$100,000. Of these 20 returns, 6 had charitable contributions of more than \$1,000. Suppose 4 of these returns are selected for a comprehensive audit.
a You should use the hypergeometric distribution is appropriate. Because
The sample is randomly drawn from a population without replacement
b. What is the probability exactly one of the four audited had a charitable deduction of more than \$1,000? (Round your answer to 4 decimal places.)
Now N=20, k=6 and n=4. So by hypergeometric formula,
P(k=1)=[C(6,1)*C(14,3)]/C(20,4)=0.4508
Probability=0.4508
c.What is the probability at least one of the audited returns had a charitable contribution of more ...

#### Solution Summary

The solution gives detailed steps on solving a series of questions on hypergeometric, binomial and uniform distribution.

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