Question

Find the indicated probability. A bank’s loan officer rates applicants for credit. The ratings are

      normally distributed with a mean of 500 and a standard deviation of 50. If an applicant is randomly           

      selected find the probability of a rating that is between 450 and 600.

Answer 1

Solution:

We are given that ratings are normally distributed.

Mean = 500

SD = 50

WE have to find P(450<X<600)

P(450<X<600) = P(X<600) – P(X<450)

Find P(X<600)

Z = (X – mean) / SD

Z = (600 – 500)/50

Z = 100/50

Z = 2

P(Z<2) = P(X<600) = 0.97725

(by using z-table)

Now, find P(X<450)

Z = (450 – 500)/50

Z = -50/50

Z = -1

P(Z<-1) = P(X<450) = 0.158655

(by using z-table)

P(450<X<600) = P(X<600) – P(X<450)

P(450<X<600) = 0.97725 - 0.158655

P(450<X<600) = 0.818595

Required probability = 0.818595