There are fourteen new jobs opening up at company seeking Computational Data Sci

Question

There are fourteen new jobs opening up at company seeking Computational Data Scientists, and 400 applicants show up for the 30 positions. To select the best 30 from among the applicants, the company gives a test that covers scientific programming skills, statistical background, and mathematical ability. The mean grade on this test turns out to be 70, and the scores have a variance of 25. Can a person who scores 89 count on getting one of the jobs? [Hint: Use Chebyshev’s theorem.] Assume that the distribution is symmetric about the mean. Explain your work.

Explanation / Answer

As u = mean = 70, and sigma = sqrt(25) = 5, then a garde of 89 is

k = (x-u)/sigma = (89-70)/5 = 3.8 standard deviations above the mean.

Hence, by Chebyshev's theorem, the percentage of scores higher than 89 is at most

1/(2k^2) = 1/(2*3.8^2) = 0.034626039

of the population. Hence, we expect at most

0.034626039*400 = 13.85 people to be higher than 89.

Hence, as there are 30 positions, YES, HE CAN COUNT ON GETTING ONE OF THE JOBS. [ANSWER]

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