Question

A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 220 and a standard deviation of 6. Find the value of the score at the 30th percentile (P30). Round your answer 2 places after the decimal point.

Answer 1

Given that,

mean =  = 220

standard deviation =  = 6

Using standard normal table,

P(Z < z) = 30%

=(Z < z) = 0.30

= P(Z < z ) = 0.30

z =-0.52   

Using z-score formula  

x = z +

x = -0.52 *6+220

x = 216.88