Completed initial questions but unsure on the graphs/ final 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.

a.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.

- No, it would not be reasonable because due to the high standard deviation compared to the mean. The standard deviation is (1.7-1.4)=0.3 for 0 minutes and 1.7-2.8 = -0.9.for 2 deviation, therefore we cannot have a negative duration of a call. This indicates that data obtained will be skewed.

b.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.

- Yes, we can use central limit theorem because we have large number of sample size that is n > 40 sample size so the sampling distribution will be normal even if the original distribution is not.

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

-CLT says it is nearly normal. CLT says that the sampling distribution should be normal if n is high enough, usually over 30 and on sample provided sampling is 60 which greater than 30.

d.Draw a well-labeled sketch to accompany your answer to question C.

e.Describe how the sketch would change if the sample size were 160 calls rather than 60 calls.