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. Find Peo, the score which separates the lower 60% from the top 40%.
Round to one decimal place.
O A. 212.7
OB. 207.8
OC. 211.3
OD. 187.5

Answer 1

Answer:

A. 212.7

Step-by-step explanation:

To find the score that separate the lower 60% from the top 40% , we need to know the z value that satisfy:

P(Z<z) = 0.6

So, using the standard normal table, we know that the z value is equal to 0.2533

Then, the score x that is equivalent to the z value 0.25 can be calculate as:

$z=\frac{x-m}{s}\\x=(z*s)+m$

Where m is the mean and s is the standard deviation. Therefore, replacing z by 0.25, m by 200 and s by 50, we get:

$x=(0.2533*50)+200\\x=212.7$