Question

The amount of time Americans spend using iPhone is closely monitored by firms such as A.C. Nielsen because this helps to determine advertising pricing for commercials

a) Do you thing the variable "weekly time spending on iPhone" would be normally distributed? If not, what shape would you expect the variable to have?

b) According to American Time Use Survey, adult Americans spend 2.35 hours per day using iPhone on a weekday. Assume that the standard deviation for "time spending using iPhone on a weekday" is 1.93 hours. If a random sample of 40 adult Americans is obtained, describe the sampling distribution of X, the mean amount of time spending iphone on a weekday.

c) Determine the probability that a random sample of 40 adult Americans results in a mean time using iPhone on a weekday of between 2 and 3 hours

Answer 1

a) We cannot say that the weekly time spending on iPhone by adult Americans is exactly normally distributed, but we can say that it is unimodal and has upper and lower tails.

b) The sampling distribution of X (the mean amount of time spending iphone on a weekday) is approximately normal according to Central Limit Theorem (CLT).

The distribution of the sample mean is .

c) The probability that a random sample of 40 adult Americans results in a mean time using iPhone on a weekday of between 2 and 3 hours is