step by step
QNT 561 Ch 7 # 46, 48, 50
46) The annual commissions earned by sales representatives of Machine Products, Inc., a manufacturer of light machinery, follow the normal probability distribution. The mean yearly amount earned is $40,000 and the standard deviation is $5,000.
A) What percent of the sales representatives earn more than $42,000 per year?
B) What percent of the sales representatives earn between $32,000 and $42,000?
C) What percent of the sales representatives earn between $32,000 and $35,000?
D) The sales manager wants to award the sales representatives who earn the largest commissions a bonus of $1,000. He can award a bonus to 20 percent of the representatives. What is the cutoff point between those who earn a bonus and those who do not?
48) According to a government study among adults in the 25- to 34-year age group, the mean amount spent per year on reading and entertainment is $1,994 (http://www.infoplease.com/ipa/A0908759.html). Assume that the distribution of the amounts spent follows the normal distribution with a standard deviation of $450.
A) What percent of the adults spend more than $2,500 per year on reading and entertainment?
B) What percent spend between $2,500 and $3,000 per year on reading and entertainment?
C) What percent spend less than $1,000 per year on reading and entertainment?
50) Fast Service Truck Lines uses the Ford Super Duty F-750 exclusively. Management made a study of the maintenance costs and determined the number of miles traveled during the year followed the normal distribution. The mean of the distribution was 60,000 miles and the standard deviation 2,000 miles.
A) What percent of the Ford Super Duty F-750s logged 65,200 miles or more?
B) What percent of the trucks logged more than 57,060 but less than 58,280 miles?
C) What percent of the Fords traveled 62,000 miles or less during the year?
D) Is it reasonable to conclude that any of the trucks were driven more than 70,000 miles? Explain.