The previous exercise mentions that the duration of your phone calls follows a distribution with mean μ = 2.8 minutes and standard deviation σ = 2.1 minutes. From a random sample of n = 45 calls, your parents computed a sample mean of x̅ = 3.4 minutes and a sample standard deviation of s = 2.9 minutes.
a. Sketch the population distribution for the duration of your phone calls. What are its mean and standard deviation?
b. What are the mean and standard deviation of the data distribution?
c. Find the mean and standard deviation of the sampling distribution of the sample mean.
d. Is the sample mean of 3.4 minutes unusually high? Find its z-score and comment.
e. Your parents told you that they will kick you off the plan when they find a sample mean larger than 3.5 minutes. How likely is this to happen?