This question has two parts. Seventy new jobs are opening up at an automobile ma

Question

This question has two parts.

Seventy new jobs are opening up at an automobile manufacturing plant, and 1000 applicants show up for the 70 positions. To select the best 70 from among the applicants, the company gives a test that covers mechanical skill, manual dexterity, and mathematical ability. The mean grade on this test turns out to be 60, and the scores have a standard deviation of 6.

a)  At most how many applicants do you expect to have a score of 84 or higher? [Hint: Use Chebyshev's theorem.] Assume that the distribution is symmetric about the mean.

b) If you get a score of 84, based on your answer in part a, can you count on getting one of the jobs? (answer yes or no and explain).

Explanation / Answer

(a) k = (84 - 60)/6 = 4

1 - (1/k^2) = 1 - (1/4^2) = 0.9375

1 - 0.9375 = 0.0625

0.0625 * 1000 = 63 applicants

(b) Yes because 63 < 70

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