The mean of a normal probability distribution is 60

1)      The mean of a normal probability distribution is 60; the standard deviation is 5. (Round your answers to 2 decimal places. Omit the % sign in your response.)

(a)

About what percent of the observations lie between 55 and 65?

  Percentage of observations

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(b)

About what percent of the observations lie between 50 and 70?

  Percentage of observations

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(c)

About what percent of the observations lie between 45 and 75?

  Percentage of observations

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2)      The Kamp family has twins, Rob and Rachel. Both Rob and Rachel graduated from college 2 years ago, and each is now earning $50,000 per year. Rachel works in the retail industry, where the mean salary for executives with less than 5 years' experience is $35,000 with a standard deviation of $8,000. Rob is an engineer. The mean salary for engineers with less than 5 years' experience is $60,000 with a standard deviation of $5,000.

(1)

Compute the z values for both Rob and Rachel. (Round your answers to 3 decimal places. Negativeamountshould be indicatedby a minussign.)

z
values

  Rob

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  Rachel

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3)      A recent article in the Cincinnati Enquirer reported that the mean labor cost to repair a heat pump is $90 with a standard deviation of $22. Montes Plumbing and Heating Service completed repairs on two heat pumps this morning. The labor cost for the first was $75 and it was $100 for the second. Assume the distribution of labor costs follows the normal probability distribution.

Compute z values for each. (Round your answers to 2 decimal places. Negativeamountshould be indicatedby a minussign.)

  For $75: Z

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  For $100: Z

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4)      According to the Internal Revenue Service, the mean tax refund for the year 2007 was $2,708. Assume the standard deviation is $650 and that the amounts refunded follow a normal probability distribution.

(a)

What percent of the refunds are more than $3,000? (Round the intermediate values to 2 decimal places. Round your answer to 2 decimal places. Omit the "%" sign in your response.)

  Percent

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(b)

What percent of the refunds are more than $3,000 but less than $3,500? (Round the intermediate values to 2 decimal places. Round your answer to 2 decimal places. Omitthe "%" sign in your response.)

  Percent

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(c)

What percent of the refunds are more than $2,500 but less than $3,500? (Round the intermediate values to 2 decimal places. Round your answer to 2 decimal places. Omitthe "%" sign in your response.)

  Percent

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5)      The SAT Reasoning Test (formerly called the Scholastic Aptitude Test) is perhaps the most widely used standardized test for college admissions in the United States. Scores are based on a normal distribution with a mean of 1500 and a standard deviation of 300. Clinton College would like to offer an honors scholarship to students who score in the top 10 percent of this test. What is the minimum score that qualifies for the scholarship?

  Minimum score

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6)      Shorty's Muffler advertises it can install a new muffler in 30 minutes or less. However, the work standards department at corporate headquarters recently conducted a study and found that 20 percent of the mufflers were not installed in 30 minutes or less. TheMaumeebranchinstalled 50 mufflerslastmonth.

If the corporate report is correct:

(a)

How many of the installations at the Maumee branch would you expect to take more than 30 minutes?

  Installation

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(b)

What is the likelihood that fewer than eight installations took more than 30 minutes? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)

  Likelihood

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(c)

What is the likelihood that eight or fewer installations took more than 30 minutes? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)

  Likelihood

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(d)

What is the likelihood that exactly 8 of the 50 installations took more than 30 minutes? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)

  Likelihood

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