Question

A recent personalized information sheet from your wireless phone carrier claims that the mean duration of all your phone calls was μ = 2.4 minutes with a standard deviation of o = 1.8 minutes. complete parts a through c below.

a. is the population distribution of the duration of your phone calls likely to be bell shaped, right, or left skewed?
b. You are on a shared wireless plan with your parents, who are statisticians. They look at some of your recent monthly statements that list each call and its duration and randomly sample 45 calls from the thousands listed there. They construct a histogram of the duration to look at the data distribution. Is this distribution likely to be bell shaped, right-, or left-skewed?
c. From the sample of n = 45 calls, your parents compute the mean duration. Is the sampling distribution of the sample mean likely to be bell shaped, right-, or left-skewed, or is it impossible to tell?

Answer 1

a. The population distribution of the duration of your phone calls is likely to be bell shaped. This is because the mean, median, and mode are all equal to 2.4 minutes. This means that the data is evenly distributed around the mean.

b. The distribution of the 45 calls is likely to be bell shaped as well. This is because the sample size is large enough to be representative of the population. Additionally, the sample was randomly selected, so it is unlikely to be biased.

c. The sampling distribution of the sample mean is also likely to be bell shaped. This is because the central limit theorem states that the sampling distribution of the sample mean will be approximately normal, regardless of the shape of the population distribution, as long as the sample size is large enough. In this case, the sample size is 45, which is large enough to satisfy the requirements of the central limit theorem.

It is important to note that the sampling distribution of the sample mean will only be exactly normal if the population distribution is normal. However, in most cases, the sampling distribution will be approximately normal, even if the population distribution is not.

Explanation: