Help!!!!

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 an applicant is randomly selected, find the probability of a rating that is between 170 and 220.

 

 

Answer 1

What you want is P(X<220)-P(X<170). A lot of technology tools will give you this directly, but if you want to convert the problem in to Z scores to use a table of the standard normal distribution, this is how you do it.

 

For X = 220 Z=(220-200)/50 = 0.4

For X = 170 Z=(170-200)/50 = -0.6

 

We want P(Z<0.4)-P(Z<-0.6) and P(Z<-0.6) = 1-P(Z<0.6). So we want P(Z<0.4) - 1 + P(Z<0.6) = Φ(0.4) + Φ(0.6) - 1= 0.7257+0.6554-1=0.3812 (I carried more digits in the computation than I have written here, so the discrepancy in the last digit is rounding.)