Question

Weekly loss amounts for the past 5 years follow a normal distribution with a mean of 400 and a variance of 2500. It is anticipated that the weekly loss amounts over the next 5 years would be similarly distributed, but they are trended up by 10% to account for inflation. Calculate the 85th percentile of the predicted weekly loss amounts over the next 5 years.

A.428

B.453

C.486

D.497

E.511

Answer 1

Solution:

The correct option is D. 497

Explanation:

We are given that the mean and standard deviation is:

Since the loss amount is trended up by 10% to account for inflation, therefore, the new mean and standard deviation will be increased by 10%

The new mean and standard deviation are:

Now to find the 85th percentile value, we have to first find the z-value corresponding to area = 0.85. Using the standard normal table, we have:

Now using the z-score formula, we have: