Question 326435: PROBLEM 1
The 2003 Zagat Restaurant Survey provides food, décor, and service ratings for some of the top restaurants
across the United States. For 15 top-ranked restaurants located in Boston, the average price of a dinner
including, one drink and tip, was $48.60. You are leaving for a business trip to Boston and will eat dinner at
three of these restaurants. Your company will reimburse you for a maximum of $50 per dinner. Business
associates familiar with these restaurants have told you that the meal cost at one-third of these restaurants
will exceed $50. Suppose that you randomly select three restaurants for dinner.
a. What is the probability that none of the meals will exceed the cost covered by your company?
b. What is the probability that one of the meals will exceed the cost covered by your company?
c. What is the probability that two of the meals will exceed the cost covered by your company?
d. What is the probability that all three of the meals will exceed the cost covered by your company?
PROBLEM 2
Military radar and missile detection system are designed to warn a country of an enemy attack. A
reliability question is whether a detection system will be able to identify an attack and issue a warning.
Assume that a particular detection system has a .90 probability of detecting a missile attack.
a. What is the probability that single detection system will detect the attack?
b. If two detection systems are installed in the same area and operating independently, what is the
probability that at least one of the systems will detect the attack?
c. If three systems are installed, what is the probability that at least one of the systems will detect
the attack?
d. Would you recommend the multiple detection systems be used? Explain.
I would recommed 3 detection systems be installed. Like a wise man says there is saftey in numbers
PROBLEM 3
Phone calls arrive at the rate of 48 per hour at the reservation desk for Regional Airways.
a. Compute the probability of receiving three calls in a 5-minute interval of time.
b. Compute the probability of receiving exactly 10 calls in 15 minutes.
c. Suppose, no calls are currently on hold. If the agent takes 5 minutes to complete the current
call, how many callers do you expect to be waiting by that time? What is the probability that
none will be waiting?
d. If no calls are currently being processed, what is the probability that the agent can take 3 minutes
for personal time without being interrupted by a call?
PROBLEM 4
Trading volume on the New York Stock Exchange is heaviest during the first half hour (early morning)
and last half hour (late afternoon) of the trading day. The early morning trading volumes (millions of
shares) for 13 days in January and February are shown here (Barron's, January 23, 2006;
February 13, 2006; and February 27, 2006)
Trading Volume (millions of shares)
163
171
174
180
194
198
201
202
211
211
212
214
265
The probability distribution of trading volume is approximately normal.
a. Compute the mean and standard deviation to use as estimates of the population mean and
standard deviation.
b. What is the probability that, on a randomly selected day, the early morning trading volume will be
less than 180 million shares?
c. What is the probability that, on a randomly selected day, the early morning trading volume will
exceed 230 million shares?
d. How many shares would have to be traded for the early morning trading volume on a particular
day to be among the busiest 5% of days?
PROBLEM 5
The average score for male golfers is 95 and the average score for female golfers is 106 (Golf Digest,
April 2006). Use these values as the population means for men and women and assume that the
population standard deviation σ = 14 strokes for both. A simple random sample of 30 male golfers
and another simple random sample of 45 female golfers will be taken.
a. Show the sampling distribution of x for male and female golfers.
b. What is the probability that the sample mean is within 3 strokes of the populations mean for the
sample of male golfers?
c. What is the probability that the sample mean is within 3 strokes of the populations mean for the
sample of female golfers?
d. In which case, part (b) or part (c), is the probability of obtaining a sample mean within 3 strokes of
the population mean higher? Why?
PROBLEM 6
Playbill magazine reported that the mean annual household income of its readers is $119,155.
(Playbill, January 2006). Assume this estimate of the mean annual household income is based on
a sample of 80 households, and based on past studies, the population standard deviation is known
to be σ = $30,000.
a. Develop a 90% confidence interval estimate of the population mean.
b. Develop a 95% confidence interval estimate of the population mean.
c. Develop a 99% confidence interval estimate of the population mean.
Answer by Fombitz(32388)   (Show Source):
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