Customers experiencing technical difficulty with their internet cable hookup

Customers experiencing technical difficulty with their internet cable hookup may call an 800 number for technical support. It takes the technician between 30 seconds to 15 minutes to resolve the problem. The distribution of this support time follows the uniform distribution.

(a)

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

  a

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  b

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(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

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(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

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(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. Omit the "%" sign in your response.)

  Percent

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(d)

Suppose we wish to find the middle 50 percent 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

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  End point 2

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A normal population has a mean of 21 and a standard deviation of 5.

(a)

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

  Z

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(b)

What proportion of the population is between 21 and 25? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)

  Proportion

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(c)

What proportion of the population is less than 17? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)

  Proportion

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Among U.S. cities with a population of more than 250,000 the mean one-way commute to work is 24.3 minutes. The longest one-way travel time is New York City, where the mean time is 38.8 minutes. Assume the distribution of travel times in New York City follows the normal probability distribution and the standard deviation is 7.7 minutes.

(a)

What percent of the New York City commutes are for less than 27 minutes? (Round the intermediate values to 2 decimal places. Round your answers to 2 decimal places. Omit the "%" sign in your response.)

  Percent

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(b)

What percent are between 27 and 35 minutes? (Round the intermediate values to 2 decimal places. Round your answers to 2 decimal places. Omit the "%" sign in your response.)

  Percent

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(c)

What percent are between 27 and 43 minutes? (Round the intermediate values to 2 decimal places. Round your answers to 2 decimal places. Omit the "%" sign in your response.)

  Percent

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Assume that the mean hourly cost to operate a commercial airplane follows the normal distribution with a mean of $2,025 per hour and a standard deviation of $195.

What is the operating cost for the lowest 3 percent of the airplanes? (Round z value to 2 decimal places. Omit the "$" sign in your response.)

For the most recent year available, the mean annual cost to attend a private university in the United States was $20,307. Assume the distribution of annual costs follows the normal probability distribution and the standard deviation is $4,275.

Ninety-five percent of all students at private universities pay less than what amount? (Round z value to 2 decimal places and your final answer to the nearest whole number. Omit the "$" sign in your response.)

Dottie's Tax Service specializes in federal tax returns for professional clients, such as physicians, dentists, accountants, and lawyers. A recent audit by the IRS of the returns she prepared indicated that an error was made on 7 percent of the returns she prepared last year. Assuming this rate continues into this year and she prepares 80 returns. What is the probability that she makes errors on:

(a)

More than 6 returns? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)

  Probability

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(b)

At least 6 returns? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)

  Probability

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(c)

Exactly 6 returns? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)

  Probability

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Waiting times to receive food after placing an order at the local Subway sandwich shop follow an exponential distribution with a mean of 52 seconds. Calculate the probability a customer waits:

(a)

Less than 32 seconds. (Round your answer to 4 decimal places.)

  Probability

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(b)

More than 120 seconds. (Round your answer to 4 decimal places.)

  Probability

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(c)

Between 40 and 65 seconds. (Round your answer to 4 decimal places.)

  Probability

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(d)

Fifty percent of the patrons wait less than how many seconds? What is the median? (Round youranswer to 2 decimal places.)

  Median

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The Bureau of Labor Statistics’ American Time Use Survey showed that the amount of time spent using a computer for leisure varied greatly by age. Individuals age 75 and over averaged .30 hour (18 minutes) per day using a computer for leisure. Individuals ages 15 to 19 spend 1.0 hour per day using a computer for leisure. If these times follow an exponential distribution, find the proportion of each group that spends:

(a)

Less than 14 minutes per day using a computer for leisure. (Round your answers to 4 decimal places.)

  Proportion

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(b)

More than two hours. (Round your answers to 4 decimal places.)

  Proportion

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(c)

Between 28 minutes and 84 minutes using a computer for leisure. (Round your answers to 4 decimal places.)

  Proportion

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(d)

Find the 28th percentile. Seventy two percent spend more than what amount of time? (Round your answers to 2 decimal places.)

  Amount of time for individuals age 75 and over

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  Amount of time for individuals ages 15 to 19

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The cost per item at a supermarket follows an exponential distribution. There are many inexpensive items and a few relatively expensive ones. The mean cost per item is $10.00. What is the percentage of items that cost:

(a)

Less than $7.00? (Round your answer to 4 decimal places.)

  Probability

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(b)

More than $11.00? (Round your answer to 4 decimal places.)

  Probability

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(c)

Between $8.00 and $10.00? (Round your answer to 4 decimal places.)

  Probability

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(d)

Find the 50th percentile. Fifty percent of the supermarket items cost more than what amount? (Round youranswer to 2 decimal places.)

  Amount

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