Question

14.  A bank’s loan officer rates applicants for credit. The ratings are normally distributed with a mean of 225 and a standard deviation of 35.

a. If one applicant is randomly chosen find the probability of a rating between 210 and 240. Round to four decimal places. (4 points)

b. The loan officer will only look at applicants that are in the top fifteen percent. Determine the rating that separates the bottom 85% from the top 15% of ratings for the applicants. (4 points)

Answer 1

Solution :

Given that ,

mean =   = 225

standard deviation = = 35   

n = 1

= 225

=  / n= 35 / 1=35

P(210<     < 240) = P[(210-225) /35 < ( - ) /   < (240-225) /35 )]

= P(-0.43 < Z <0.43 )

= P(Z < 0.43) - P(Z < -0.43)

Using z table

=0.6664-0.3336

=0.3328

probability= 0.3328

b)

P(Z < z) = 85%

= P(Z < z) = 0. 85

= P(Z < ) = 0. 85

z = 1.04 Using standard normal z table,

Using z-score formula  

x= z * +

x=1.04 *35+225

x= 261.4