A bank's loan officer rates applicants for credit. the ratings are normally distributed with a mean of 200 and a standard deviation of 50. if 40 different applicants are randomly selected, find the probability that their mean is above 215. round your answer to four decimal places.

Question

Mathematics

Jaslene Spencer

1 December, 10:45

A bank's loan officer rates applicants for credit. the ratings are normally distributed with a mean of 200 and a standard deviation of 50. if 40 different applicants are randomly selected, find the probability that their mean is above 215. round your answer to four decimal places.

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Zaire Bird · Answer 1

Given data shows that mean of 200 and a standard deviation of 50. The probability that their mean is above 215 is calcualted by : (215-200) / [50/sqrt (40) ] = 1.8974 P (x-bar > 215) = P (z > 1.8974) = normalcdf (1.8974,100) = 0.0289. if 40 different applicants are randomlyâ€‹ selected, the probability that their mean is above 215 will be 0.0289.