Question

The length of mobile phone calls for teenagers is known to be normally distributed, with a mean calling time of 5 minutes and a standard deviation of 1.5 minutes. If a random sample of 36 phone calls is selected, what is the probability that the sample average time spent on calls is between 4.25 minutes and 5.75 minutes (four decimal places)?

Answer 1

Given the length of mobile phone calls for teenagers is known to be normally distributed, with a mean calling time of = 5 minutes and a standard deviation of =1.5 minutes.

Thus to calculate the probability of standard normal distribution we need to find the Z score, a random sample of n = 36 phone calls is selected.

Now the probability that the sample average time spent on calls is between = 4.25 minutes and = 5.75 minutes is calculated by finding the Z scores at the average time spent on call as:

Thus the probability P(4.25 < < 5.75) is P( -3 < Z < 3) is calculated uisng the excel formula for normal distribution which is =NORM.S.DIST(3, TRUE)-NORM.S.DIST(-3, TRUE), thus the probability is computed as:

=> 0.9987−0.0013

=> 0.9973.