Question

The durations of phone calls taken by the receptionist at an office are like draws made at random with replacement from a list that has an average of 8.5 minutes (that's 8 minutes and 30 seconds) and an SD of 3 minutes. Approximately what is the chance that the total duration of the next 100 calls is more than 15 hours?

Answer 1

First convert everything into seconds.

The mean is 8.5 minutes for one call, so it's 100 times that amount for 100 calls.

The SD is 3 minutes, the variance is the SD squared. Multiply that variance by 100, then take the square root of it for the SD for 100 calls.

\[\Large z = \frac{ x - mean }{ SD }\]
x is the time for 100 calls, put it in seconds (x = 15 hours, 54000 seconds). The mean is the mean for 100 calls, SD is the SD for 100 calls. You'll use the z score to find the probability, use this normal curve:
http://www.mathsisfun.com/data/standard-normal-distribution-table.html

P ( X > 54,000) =

Answer 2

0.04779