PROBLEM 1: Packer Fan Tours is the official tour company for the Green Bay Packers of the NFL. One of the events in the package is to sponsor a reception the night before a game for fans that is attended by 3 of the players from the team. There are 53 players on the Green Bay Packers' roster of which 22 are starters. Assume that the 3 players attending the reception this week are chosen randomly. Determine the probability of the following occurring:
a. None of the players at the reception are starters.
b. All of the players at the reception are starters.
c. One of the players at the reception are starters.
d. Two of the players at the reception are starters.
PROBLEM 2: Fourteen of the top twenty finishers in the 2009 PGA Championship at Hazeltine National Golf Club in Chaska, Minnesota, used a Titleist brand golf ball (GolfBalTest website, November 12, 2009). Suppose these results are representative of the probability that a randomly selected PGA Tour player uses a Titleist brand golf ball. For a sample of 22 PGA Tour players, Make the following calculations:
a. Compute the probability that exactly 11 of the 22 PGA Tour players use a Titleist brand golf ball.
b. Compute the probability that more than 13 of the 22 PGA Tour players use a Titleist brand golf ball.
c. Compute the probability that less than 9 of the 22 PGA Tour players use a Titleist brand golf ball.
d. For a sample of 22 PGA Tour players, compute the expected number of players who use a Titleist brand golf ball.
e. For a sample of 22 PGA Tour players, compute the standard deviation of the number of players who use a Titleist brand golf ball.
PROBLEM 3: Customers arrive at a local ice cream stand at an average rate of 16 per hour.
a. What is the probability that 2 customers will arrive during the next 15 minutes?
b. What is the probability that 4 customers will arrive during the next 15 minutes?
c. What is the probability that 6 customers will arrive during the next 30 minutes?
d. What is the probability that 6 customers will arrive during the next 45 minutes?
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 15 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)
214
202
174
187
163
198
171
265
222
212
211
194
201
211
180
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 195 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: According to the Organization for Economic Co-Operation and Development (OECD), adults in the United States worked an average of 1,790 hours in 2007. Assume the population standard deviation is 400 hours and that a random sample of 50 U.S. adults was selected.
a. Calculate the standard error of the mean.
b. What is the probability that the sample mean will be more than 1,800 hours?
c. What is the probability that the sample mean will be between 1,750 and 1,840 hours?
d. Would a sample mean of 1,825 hours support the claim made by the OECD? Explain?
PROBLEM 6: Playbill magazine reported that the mean annual household income of its readers is $122,550. (Playbill, January 2006). Assume this estimate of the mean annual household income is based on a sample of 85 households, and based on past studies, the population standard deviation is known to be σ = $32,500.
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.
d. Discuss what happens to the width of the confidence interval as the confidence level is increase. Does this result seem reasonable? Explain.
PROBLEM 7: Travelocity would like to estimate the current average domestic airfare. The data in column A shows the airfares for 26 randomly selected tickets for travel within the United States.
Airfares
356
414
320
303
275
367
244
489
371
362
370
251
384
286
215
361
457
104
322
278
358
337
326
136
409
265
a. Provide a point estimate of the population mean for airfares in the United States.
b. At 95% confidence, what is the margin of error?
c. What is the 95% confidence interval estimate of the population mean?
PROBLEM 8: The travel-to-work time for residents of the 25 largest cities in the United States is reported in the 2003 Information Please Almanac. Suppose that a preliminary simple random sample of residents of San Francisco is used to develop a planning value of 6.25 minutes for the population standard deviation.
a. If we want to estimate the population mean travel-to-work for San Francisco residents with a margin of error of 3 minutes, what sample size should be used? Assume 95% confidence.
b. If we want to estimate the population mean travel-to-work for San Francisco residents with a margin of error of 30 seconds, what sample size should be used? Assume 99% confidence.