Question

Suppose that a phone company reports that the average duration of a cell phone call is
1.7 minutes, with a standard deviation of 1.4 minutes.


1. Would it be reasonable to use a normal distribution to model the duration of cell phone calls? Explain, based primarily on the values reported above.



2. Suppose you want to examine a random sample of 60 cell phone calls. Do you think it would be reasonable to use the Central Limit Theorem to describe the sampling distribution of the sample mean call duration? Explain.


3. What does the CLT say about the sampling distribution of the sample mean call duration in a random sample of 60 calls?

Answer 1

1. Probably not, due to the high standard deviation as compared to the mean.

2. Yes, because you have a large enough sample so the sampling distribution will be normal even if the original distribution is not.

3. The CLT says that the sampling distribution should be normal if n is high enough, usually over 30. 60 is certainly big enough for the sampling distribution to be normal.

Answer 2

1. No. 1 standard deviation is within .3 of 0 minutes (1.7-1.4) and 2 deviations is 1.7-2.8 = -0.9. We obviously cannot have a negative duration for a call. The distributtion is skewed and there is too much of a probability (slightly more than 1 deviation from the mean) that the durations are negative.

2. Yes. The sample size is greater than 40. If there are no outliers, it would be reasonable. The central limit theorem says that the distributtion of the sampling mean will be nearly normal.

3. It is nearly normal.