88. Refer to the Baseball 2005 data, which reports information on the 30 major league teams for the 2005 baseball season.
a. Select the variable team salary and find the mean, median, and the standard deviation.
b. Select the variable that refers to the age the stadium was built. (Hint: Subtract the
year in which the stadium was built from the current year to find the stadium age and
work with that variable.) Find the mean, median, and the standard deviation.
c. Select the variable that refers to the seating capacity of the stadium. Find the mean,
Median, and the standard deviation.
56. Assume the likelihood that any flight on Northwest Airlines arrives within 15 minutes of the scheduled time is .90. We select four flights from yesterday for study.
a. What is the likelihood all four of the selected flights arrived within 15 minutes of the scheduled time?
b. What is the likelihood that none of the selected flights arrived within 15 minutes of
the scheduled time?
c. What is the likelihood at least one of the selected flights did not arrive within 15 minutes of the scheduled time?
64. An internal study by the Technology Services department at Lahey Electronics revealed company employees receive an average of two emails per hour. Assume the arrival of these emails is approximated by the Poisson distribution.
a. What is the probability Linda Lahey, company president, received exactly 1 email
between 4 P.M. and 5 P.M. yesterday?
b. What is the probability she received 5 or more email during the same period?
c. What is the probability she did not receive any email during the period?
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.
38. The mean amount purchased by a typical customer at Churchill’s Grocery Store is $23.50 with a standard deviation of $5.00. Assume the distribution of amounts purchased follows the normal distribution. For a sample of 50 customers, answer the following questions.
a. What is the likelihood the sample mean is at least $25.00?
b. What is the likelihood the sample mean is greater than $22.50 but less than $25.00?
c. Within what limits will 90 percent of the sample means occur
54. Families USA, a monthly magazine that discusses issues related to health and health costs, surveyed 20 of its subscribers. It found that the annual health insurance premiums for a family with coverage through an employer averaged $10,979. The standard deviation of the sample was $1,000.
a. Based on this sample information, develop a 90 percent confidence interval for the
population mean yearly premium.
b. How large a sample is needed to find the population mean within $250 at 99 percent confidence?
42. During recent seasons, Major League Baseball has been criticized for the length of the games. A report indicated that the average game lasts 3 hours and 30 minutes. A sample of 17 games revealed the following times to completion. (Note that the minutes have been changed to fractions of hours, so that a game that lasted 2 hours and 24 minutes is reported at 2.40 hours.)
2.98 2.40 2.70 2.25 3.23 3.17 2.93 3.18 2.80
2.38 3.75 3.20 3.27 2.52 2.58 4.45 2.45
Can we conclude that the mean time for a game is less than 3.50 hours? Use the .05
58. The amount of income spent on housing is an important component of the cost of living.
The total costs of housing for homeowners might include mortgage payments, property
taxes, and utility costs (water, heat, electricity). An economist selected a sample of
20 homeowners in New England and then calculated these total housing costs as a percent
of monthly income, five years ago and now. The information is reported below. Is it
reasonable to conclude the percent is less now than five years ago?
Homeowner Five Years Ago Now Homeowner Five Years Ago Now
1 17% 10% 11 35% 32%
2 20 39 12 16 32
3 29 37 13 23 21
4 43 27 14 33 12
5 36 12 15 44 40
6 43 41 16 44 42
7 45 24 17 28 22
8 19 26 18 29 19
9 49 28 19 39 35
10 49 26 20 22 12
42. Martin Motors has in stock three cars of the same make and model. The president would like to compare the gas consumption of the three cars (labeled car A, car B, and car C) using four different types of gasoline. For each trial, a gallon of gasoline was added to an empty tank, and the car was driven until it ran out of gas. The following table shows the number of miles driven in each trial.
Types of Gasoline Car A Car B Car C
Regular 22.4 20.8 21.5
Super regular 17.0 19.4 20.7
Unleaded 19.2 20.2 21.2
Premium unleaded 20.3 18.6 20.4
Using the .05 level of significance:
a. Is there a difference among types of gasoline?
b. Is there a difference in the cars?
37. A regional commuter airline selected a random sample of 25 flights and found that the correlation between the number of passengers and the total weight, in pounds, of luggage stored in the luggage compartment is 0.94. Using the .05 significance level, can we conclude that there is a positive association between the two variables?
40. A suburban hotel derives its gross income from its hotel and restaurant operations. The owners are interested in the relationship between the number of rooms occupied on a nightly basis and the revenue per day in the restaurant. Below is a sample of 25 days (Monday through Thursday) from last year showing the restaurant income and number of rooms occupied
Day Income Occupied Day Income Occupied
1 $1,452 23 14 $1,425 27
2 1,361 47 15 1,445 34
3 1,426 21 16 1,439 15
4 1,470 39 17 1,348 19
5 1,456 37 18 1,450 38
6 1,430 29 19 1,431 44
7 1,354 23 20 1,446 47
8 1,442 44 21 1,485 43
9 1,394 45 22 1,405 38
10 1,459 16 23 1,461 51
11 1,399 30 24 1,490 61
12 1,458 42 25 1,426 39
13 1,537 54
Use a statistical software package to answer the following questions.
a. Does the breakfast revenue seem to increase as the number of occupied rooms
increases? Draw a scatter diagram to support your conclusion.
b. Determine the coefficient of correlation between the two variables. Interpret the value.
c. Is it reasonable to conclude that there is a positive relationship between revenue and
occupied rooms? Use the .10 significance level.
d. What percent of the variation in revenue in the restaurant is accounted for by the number of rooms occupied?
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