Question

A bank's loan officer rates applicants fro credit. The ratings are normally distributed with a mean of 600 and a standard deviation of 50. If 40 applicants are randomly selected, find the probability that their mean credit score is more than 575. Round to 4-decimal places.

Answer 1

Solution :

Given that,

mean = = 600

standard deviation = = 50

= =600

= / n = 50/ 40 = 7.9

P( > 575) = 1 - P( <575 )

= 1 - P[( - ) / < (575-600) / 7.9]

= 1 - P(z < -3.16)

Using z table

= 1 - 0.0008

= 0.9992

probability= 0.9992