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Suppose we know that the ages of employees in Industries A, B, and C are normally distributed. We are given the following information on the relevant parameters: Graphically compare the ages of employees in Industry A with Industry B. Repeat the comparison for Industry A with Industry C.
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WHAT IS THE STANDARD NORMAL DISTRIBUTION?
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a) Find the following probabilities for the standard normal random variable Z. b) P(0 ≤ Z ≤ 1.96) c) P(1.52 ≤ Z ≤ 1.96) d) P(−1.52 ≤ Z ≤ 1.96) e) P(Z > 4)
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WHAT IS THE STANDARD TRANSFORMATION: CONVERTING X INTO Z?
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Scores on a management aptitude exam are normally distributed with a mean of 72 and a standard deviation of 8. What is the probability that a randomly selected manager will score above 60? What is the probability that a randomly selected manager will score between 68 and 84?
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WHAT IS THE INVERSE TRANSFORMATION: CONVERTING Z INTO X?
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Scores on a management aptitude examination are normally distributed with a mean of 72 and a standard deviation of 8. a. What is the lowest score that will place a manager in the top 10% (90th percentile) of the distribution? b. What is the highest score that will place a manager in the bottom 25% (25th percentile) of the distribution?
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We can now answer the questions first posed by Akiko Hamaguchi in the introductory case of this chapter. Recall that Akiko would like to buy the right amount of salmon for daily consumption at Little Ginza. Akiko has estimated that the daily consumption of salmon is normally distributed with a mean of 12 pounds and a standard deviation of 3.2 pounds. She wants to answer the following questions: a) What is the probability that the demand for salmon at Little Ginza is above 20 pounds? b) What is the probability that the demand for salmon at Little Ginza is below 15 pounds? c) How much salmon should be bought so that it meets customer demand on 90% of the days?
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