Question

Answers claims that the mean length of all cell phone conversations in the United States is 3.25 minutes (3 minutes and 15 seconds). Assume that this is correct, and also assume that the standard deviation is 4.2 minutes. Suppose that, using a phone company’s records, we randomly sample 100 phone calls and make a histogram of the length of 100 phone calls. Is this histogram a display of the population distribution, the distribution of a sample, or the sampling distribution of means?

Answer 1

Explanation:

a)

As the mean is less than the standard deviation, then this seems to be right skewed. [ANSWER]

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b)

By central limit theorem, this distribution has the same mean as the original population.

u(X) = u = 3.25 [ANSWER]

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c)

By central limit theorem, it will have a reduced standard deviation,

sigma(X) = sigma/sqrt(n) = 4.2/sqrt(100) = 0.42 [ANSWER]