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 HDMI Digital Antenna systems ranged from about $25 to $200 (source: “Everything you need to know about replacing cable with an HDTV antenna,” www.fool.com, June 27, 2015). The file titled HDCosts contains a sample of the total costs including installation for HDMI Digital Antenna systems. 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 would be more than $5 different 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.