Question

Electricity bills in a certain city have a mean 87.73. Assume the bills are normally distributed with standard deviation $12.27. A sample of 61bills was selected for an audit. Find the 48 percentile for the sample mean.

Answer 1

Let ,

Since , n=61

Now , the distribution of the sample mean is ,

Therefore , the 48 th percentile is ,

..........(1)

Now , ..............(2); from normal probability table

From (1) and (2)

Therefore , the 48 percentile for the sample mean is 87.6515