Bruce Leichtman is president of Leichtman Research Group, Inc. (LRG), which specializes in research and consulting on broadband, media, and entertainment industries. In a recent survey, the company determined the cost of extra high-definition (HD) gear needed to watch television in HD. The costs ranged from $5 a month for a set-top box to $200 for a new satellite. The file titled HDCosts contains a sample of the cost of the extras whose purchase was required to watch television in HD. Assume that the population average cost is $150 and the standard deviation is $50.
a. Create a box and whisker plot and use it and the sample average to determine if the population from which this sample was obtained could be normally distributed.
b. Determine the probability that the mean of a random sample of size 150 costs for HD extras would be more than $5 away from the mean of the sample described above.
c. Given your response to part a, do you believe the results obtained in part b are valid? Explain.