1. In December 1997, the U.S. Department of Justice issued an injunction against Microsoft
Corporation for bundling its Internet Explorer Web browser with its Windows 95 operating
system {Fortune, February 2, 1998). Public opinion was divided on whether Microsoft was a
monopoly.
In a Fortune poll, 41% of respondents agreed with the statement. "Microsoft is a monopoly."
a. For a sample of 800 people, how many would you expect to agree that Microsoft is a
monopoly?
b. For a sample of 800 people, what is the probability that 300 or fewer agree that Micro
soft is a monopoly?
c. Again for a sample of 800 people, what is the probability that more than 450 do not
agree that Microsoft is a monopoly?
2. A Myrtle Beach resort hotel has 120 rooms. In the spring months, hotel room occupancy
is approximately 75%.
a. What is the probability that at least half of the rooms are occupied on a given day?
b. What is the probability that 100 or more rooms are occupied on a given day?
c. What is the probability that 80 or fewer rooms are occupied on a given day?
3. Sixty-eight percent of the debt owed by American families is home mortgage or equity
credit (Federal Reserve Bulletin, January 1997). The median amount of mortgage debt for
families with the head of the household under 35 years old is $63,000. Assume the amount
of mortgage debt for this group is normally distributed and the standard deviation is $15,000.
a. What is the mean amount of mortgage debt for this group?
b. How much mortgage debt do the 10% with the smallest debt have?
c. What percent of these families have mortgage debt in excess of $80,000?
d. The upper 5% of mortgage debt is in excess of what amount?
4. Motorola used the normal distribution to determine the probability of defects and the num-
ber of defects expected in a production process (APICS—The Performance Advantage,
July 1991). Assume a production process produces items with a mean weight of 10 ounces.
Calculate the probability of a defect and the expected number of defects for a 1000-unit
production run in the following situations.
a. The process standard deviation is .15, and the process control is set at plus or minus
one standard deviation. Units with weights less than 9.85 or greater than 10.15 ounces
will be classified as defects,
b. Through process design improvements, the process standard deviation can be reduced to
.05. Assume the process control remains the same, with weights less than 9.85 or greater
than 10.15 ounces being classified as defects.
c. What is the advantage of reducing process variation thereby setting process control limits
at a greater number of standard deviations from the mean?
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