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 Upper P 60, the score which separates the lower 60% from the top 40%. Round to one decimal place.

Upper P60 = 212.8

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

Find Upper P 60, the score which separates the lower 60% from the top 40%.

This is the value of X when Z has a pvalue of 0.6. So it is X when Z = 0.255.

Upper P60 = 212.8