Question

The first step of a certain job application process is an exam. The exam is worth 100 points. The scores on the exam were normally distributed, with a mean score of 76 points and a standard deviation of 4.2 points. Last year, there were 440 applications. Of the 440 applicants, those with a minimum score of 68 points qualified to advance to the second step of the application process. The reference table lists z-scores and the associated cumulative probabilities.



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Approximately how many applicants advanced to the second step? Record your answer as a whole number.

Answer 1

z = (68 - 76)/4.2 = -8/4.2 ≈ -1.905.
Phi(-1.905) ≈ 0.0284, so P(score ≥ 68) = 1 − 0.0284 = 0.9716.
Expected number = 0.9716 × 440 ≈ 427.54 ≈ 428.

Approximately 428 applicants advanced.