Question: The owner of a mail-order catalog would like to compare her sales with geographic distribution of the population. According to the U.S. Bureau of Census, 21% of the population lives in the Northeast, 24% in the Midwest, 35% in the South, and 20% in the West. Listed below is a breakdown of a sample of 400 orders randomly selected from those shipped last month. At the .01 significance level, does the distribution of the orders reflect the population?

Region Frequency

Northeast 68
Midwest 104
South 155

West 73

Total 400

Advertising expenses are a significant component of the cost of goods sold. Listed below is a frequency distribution showing the advertising expenditures for 60 manufacturing companies located in the Southwest. The mean expense is $52.0 million and the standard deviation is $11.32 million. Is it reasonable to conclude the sample data are from a population that follows a normal probability distribution? Use the 0.5 significance level.

Advertising Expense ($Million) Number of Companies

25 up to 35 5
35 up to 45 10
45 up to 55 21
55 up to 65 16

65 up to 75 8

Total 60