Question

A large manufacturing firm tests job applicants who recently graduated from colleges. The test scores are normally distributed with a mean of 500 and a standard deviation of 50. If an applicant is selected at random, what is the probability that he/she has a score between 438 and 604?

Answer 1

Let,

Score of the candidate be x

Mean, M = 500

Standard deviation, s = 50

Probability that score of the randomly selected applicant is between 438 and 604

P( 438 < x < 604)

=> P ( (438-M)/s < (x-M)/s < (604-M)/s))

=> P( (438-500)/50 < z < (604-500)/50)

=> P(-1.24 < z < 2.08) = P(z< 2.08) - P(z < -1.24)

=> Probability = 0.9812 - 0.1075 = 0.8737

Thus, probablity that the score of the randomly selected applicant lies between 604 and 438 is 87.37%.

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