In: Statistics and Probability
A bank's loan officer rates applicants fro credit. The ratings are normally distributed with a mean of 620 and a standard deviation of 50. If 40 applicants are randomly selected, find the probability that their mean credit score is between 575 and 630. Round to 4-decimal places.
Solution :
Given that ,
mean = = 620
standard deviation = = 50
n = 40
= 620
= / n= 50/ 40=7.9057
P(575< <630 ) = P[(575-620) / 7.9057 < ( - ) / < (630-620) / 7.9057 )]
= P( -5.69< Z <1.26 )
= P(Z <1.26 ) - P(Z < -5.69)
Using z table
=0.8962-0
=0.8962
probability= 0.8962