Question

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 16 different applicants are randomly selected, find the probability that their mean is above 215. Round to 3 decimals.

Answer 1

Mean, = 200

Standard deviation, = 50

Sample size, n = 16

Sampling distribution of mean has mean = = 200

Standard error = =

=

= 12.5

P( < A) = P(Z < (A - )/)

P(mean is above 215) = P( > 215)

= 1 - P( < 215)

= 1 - P(Z < (215 - 200)/12.5)

= 1 - P(Z < 1.2)

= 1 - 0.8849

= 0.115