Question: If a random variable Y is normally distributed with mean \(\mu \) and standard deviation \(\sigma \) he Z ratio \(\frac{Y-\mu }{\sigma }\) is often referred to as a normed score: It indicates the magnitude of y relative to the distribution from which it came. " Norming" is sometimes used as an affirmative action mechanism in hiring decisions. Suppose a cosmetics company is seeking a new sales manager. The aptitude test they have traditionally given for that position shows a distinct gender bias: Scores for men are normally distributed with \(\mu \) = 62.0 and \(\sigma \) = 7.6, while scores for women are normally distributed with \(\mu \) = 76.3 and \(\sigma \) = 10.8. Laura and Michael are the two candidates vying for the position: Laura has scored 92 on the test and Michael 75. If the company agrees to norm the scores for gender bias, whom should they hire?

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