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.

Admissions

Probability

1,060

0.5

1,300

0.2

1,640

0.3

1.

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

Expected number of admissions

2.

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

Variance

Standard deviation

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2.

The Internal Revenue Service is studying the category of charitable contributions. A sample of 25 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 25 returns, 5 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

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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 27 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

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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 12 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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5.

A normal population has a mean of 22 and a standard deviation of 5.

a.

Compute the z value associated with 25. (Round your answer to 2 decimal places.)

Z

b.

What proportion of the population is between 22 and 25? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)

Proportion

c.

What proportion of the population is less than 18? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)

Proportion

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6.

Assume that the hourly cost to operate a commercial airplane follows the normal distribution with a mean of $2,306 per hour and a standard deviation of $258.

What is the operating cost for the lowest 1% of the airplanes? (Round z value to 2 decimal places and round final answer to nearest whole dollar.)

Operating cost

$

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7.

The manufacturer of a laser printer reports the mean number of pages a cartridge will print before it needs replacing is 12,275. The distribution of pages printed per cartridge closely follows the normal probability distribution and the standard deviation is 745 pages. The manufacturer wants to provide guidelines to potential customers as to how long they can expect a cartridge to last.

How many pages should the manufacturer advertise for each cartridge if it wants to be correct 99 percent of the time? (Round z value to 2 decimal places. Round your answer to the nearest whole number.)

Pages

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8.

A study of long-distance phone calls made from General Electric Corporate Headquarters in Fairfield, Connecticut, revealed the length of the calls, in minutes, follows the normal probability distribution. The mean length of time per call was 3.50 minutes and the standard deviation was 0.70 minutes.

a.

What fraction of the calls last between 3.50 and 4.00 minutes? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)

Fraction of calls

b.

What fraction of the calls last more than 4.00 minutes? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)

Fraction of calls

c.

What fraction of the calls last between 4.00 and 5.00 minutes? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)

Fraction of calls

d.

What fraction of the calls last between 3.00 and 5.00 minutes? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)

Fraction of calls

e.

As part of her report to the president, the director of communications would like to report the length of the longest (in duration) 3 percent of the calls. What is this time? (Round z-score computation to 2 decimal places and your final answer to 2 decimal places.)

Duration

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9.

A population consists of the following five values: 12, 14, 16, 18, and 22.

a.

List all samples of size 3, and compute the mean of each sample. (Round your mean value to 2 decimal places.)

Sample

Values

Sum

Mean

1

2

3

4

5

6

7

8

9

10

b.

Compute the mean of the distribution of sample means and the population mean. (Round your answers to 2 decimal places.)

Sample means

Population mean

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The mean age at which men in the United States marry for the first time follows the normal distribution with a mean of 24.1 years. The standard deviation of the distribution is 2.5 years.

For a random sample of 66 men, what is the likelihood that the age at which they were married for the first time is less than 24.6 years? (Round z value to 2 decimal places. Round your answer to 4 decimal places.)