answer.com claims that the mean length of all cell phone conversations in the un
ID: 3132529 • Letter: A
Question
answer.com claims that the mean length of all cell phone conversations in the united states is 3.25minutes (3 mins and 15 sec). Assume that this is correct, and also assume that the standard deviation is 4.2 minutes.
a.) describe the shape of distribution of the length of cell phone conversations in this population. Do you expect it to be approximately normally distrbuted, right skewed, or left skewed? explain your answer.
b.) suppose that, using a phone company's records we randomly sample 100 phone calls. we calculate the mean length from this sample and record the value. we repeat this thousands of times. what will be the approximate mean value of the distribution of these thousands of sample means?
c.) refer to part b. what will be the standard deviation of this distribution of thousands of sample mean?
Explanation / Answer
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]
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