31. The board of directors of a small company consists of five people.
Three of those are ?strong leaders.? If they buy an idea, the entire
board will agree. The other ?weak? members have no influence. Three
salesmen are scheduled, one after the other, to make sales
presentations to a board member of the salesman?s choice. The salesmen
are convincing but do not know who the ?strong leaders? are. However,
they will know who the previous salesmen spoke to. The first salesman
to find a strong leader will win the account. Do the three salesmen
have the same chance of winning the account? If not, find their
respective probabilities of winning.
50. Berdine?s Chicken Factory has several stores in the Hilton Head,
South Carolina, area. When interviewing applicants for server
positions, the owner would like to include information on the amount
of tip a server can expect to earn per check (or bill). A study of 500
recent checks indicated the server earned the following tip.
Amount of Tip Number
$ 0 up to $ 5 200
5 up to 10 100
10 up to 20 75
20 up to 50 75
50 or more 50
Total 500
a. What is the probability of a tip of $50 or more?
b. Are the categories ?$0 up to $5,? ?$5 up to $10,? and so on
considered mutually exclusive?
c. If the probabilities associated with each outcome were totaled,
what would that total be?
d. What is the probability of a tip of up to $10?
e. What is the probability of a tip of less than $50?
26. A population consists of 15 items, 10 of which are acceptable. In
a sample of 4 items, what is the probability that exactly 3 are
acceptable? Assume the samples are drawn without replacement.
16. A normal population has a mean of 80.0 and a standard deviation of 14.0.
a. Compute the probability of a value between 75.0 and 90.0.
b. Compute the probability of a value 75.0 or less.
c. Compute the probability of a value between 55.0 and 70.0.
23. The commercial banks in Region III are to be surveyed. Some of
them are very large, with assets of more than $500 million; others are
medium-sized, with assets between $100 million and $500 million; and
the remaining banks have assets of less than $100 million. Explain how
you would select a sample of these banks.
7. Bob Nale is the owner of Nale?s Texaco GasTown. Bob would like to
estimate the mean number of gallons of gasoline sold to his customers.
From his records, he selects a random sample of 60 sales and finds the
mean number of gallons sold is 8.60 and the standard deviation is 2.30
gallons.
a. What is the point estimate of the population mean?
b. Develop a 99 percent confidence interval for the population mean.
c. Interpret the meaning of part b.
17. The Rocky Mountain district sales manager of Rath Publishing,
Inc., a college textbook publishing company, claims that the sales
representatives make an average of 40 sales calls per week on
professors. Several reps say that this estimate is too low. To
investigate, a random sample of 28 sales representatives reveals that
the mean number of calls made last week was 42. The standard deviation
of the sample is 2.1 calls. Using the .05 significance level, can we
conclude that the mean number of calls per salesperson per week is
more than 40?
13. The null and alternate hypotheses are:
H0: _1 _ _2
H1: _1 _ _2
A random sample of 10 observations from one population revealed a
sample mean of 23 and a sample deviation of 4. A random sample of 8
observations from another population revealed a sample mean of 26 and
a sample standard deviation of 5. At the .05 significance level, is
there a difference between the population means? |
