|m244||Banner Mattress and Furniture Company wishes to study the number of credit applications received per day for the last 300 days. The sample information is reported below.
Number of Credit Frequency
Applications (Number of Days)
0 ............... 50
1 ............... 77
2 ............... 81
3 ............... 48
4 ............... 31
5 or more .............. 13
To interpret, there were 50 days on which no credit applications were received, 77 days on which only one application was received, and so on. Would it be reasonable to conclude that the population distribution is Poisson with a mean of 2.0? Use the .05 significance level.||
|m245||Bardi Trucking Co., located in Cleveland, Ohio, makes deliveries in the Great Lakes region, the Southeast, and the Northeast. Jim Bardi, the president, is studying the relationship between the distance a shipment must travel and the length of time, in days, it takes the shipment to arrive at its destination. To investigate, Mr. Bardi selected a random sample of 20 shipments made last month. Shipping distance is the independent variable and shipping time is the dependent variable. The results are as follows:
a. Draw a scatter diagram. Based on these data, does it appear that there is a relationship between how many miles a shipment has to go and the time it takes to arrive at its destination?
b. Determine the correlation coefficient. Can we conclude that there is a positive correlation between distance and time? Use the .05 significance level.
c. Determine and interpret the coefficient of determination.
d. Determine the standard error of estimate.
e. Would you recommend using the regression equation to predict shipping time? Why or whynot.||
|m246||A batch of 25 injection-molded parts contains 5 that have suffered excessive shrinkage.
(a) If two parts are selected at random, and without replacement, what is the probability that the second part selected is one with excessive shrinkage?
(b) If three parts are selected at random, and without replacement, what is the probability that the third part selected is one with excessive shrinkage?||
|m247||A batch of 500 containers for frozen orange juice contains 5 that are defective. Two are selected, at random, without replacement from the batch.
(a) What is the probability that the second one selected is defective given that the first one was defective?
(b) What is the probability that both are defective?
(c) What is the probability that both are acceptable?||
|m248||A batch of 500 containers for frozen orange juice contains 5 that are defective. Two are selected, at random, without replacement, from the batch. Let A and B denote the events that the first and second container selected is defective, respectively.
(a) Are A and B independent events?
(b) If the sampling were done with replacement, would A and B be independent?||
|m249||A batch of 500 machined parts contains 10 that do not conform to customer requirements. The random variable is the number of parts in a sample of 5 parts that do not conform to customer requirements.||
|m250||A batch of 500 machined parts contains 10 that do not conform to customer requirements. Parts are selected successively, without replacement, until a nonconforming part is obtained. The random variable is the number of parts selected.||
|m251||Batches that consist of 50 coil springs from a production process are checked for conformance to customer requirements. The mean number of nonconforming coil springs in a batch is 5. Assume that the number of nonconforming springs in a batch, denoted as X, is a binomial random variable.
(a) What are n and p?
(b) What is P(X < 2?
(c) What is P(X > 49?||
|m252||Because not all airline passengers show up for their reserved seat, an airline sells 125 tickets for a flight that holds only 120 passengers. The probability that a passenger does not show up is 0.10, and the passengers behave independently.
(a) What is the probability that every passenger who shows up can take the flight?
(b) What is the probability that the flight departs with empty seats?||
|m253||Before banks issue a credit card, they usually rate or score the customer in terms of his or her projected probability of being a profitable customer. A typical scoring table appears below.
The score is the sum of the points on the six items. For example, Sushi Brown is under 25 years old (12 pts.), has lived at the same address for 2 years (0 pts.), owns a 4-year-old car (13 pts.), with car payments of $75 (6 pts.), housing cost of $200 (10 pts.), and a checking account (3 pts.). She would score 44.
A second chart is then used to convert scores into the probability of being a profitable customer. A sample chart of this type appears below.
Sushi’s score of 44 would translate into a probability of being profitable of approximately .81. In other words, 81% of customers like Sushi will make money for the bank card operations.
Here are the interview results for three potential customers.
1. Score each of these customers and estimate their probability of being profitable.
2. What is the probability that all three are profitable?
3. What is the probability that none of them are profitable?
4. Find the entire probability distribution for the number of profitable customers among this group of three.
5. Write a brief summary of yourfindings.||
|m254||Belk Department Store is having a special sale this weekend. Customers charging purchases of more than $50 to their Belk credit card will be given a special Belk Lottery card.
The customer will scratch off the card, which will indicate the amount to be taken off the total amount of the purchase. Listed below are the amount of the prize and the percent of the time that amount will be deducted from the total amount of the purchase.
Prize Amount Probability
$ 10 ...... .50
25 ...... .40
a. What is the mean amount deducted from the total purchase amount?
b. What is the standard deviation of the amount deducted from the total purchase?||
|m255||Below are the prices of toothpaste (9 oz.), shampoo (7 oz.), cough tablets (package of 100), and antiperspirant (2 oz.) for August 2000 and August 2013. Also included are the quantity purchased. Use August 2000 as the base.
a. Determine the simple price indexes.
b. Determine the simple aggregate price index price index. for the two years.
c. Determine Laspeyres price index.
d. Determine the Paasche
e. Determine Fisher’s idealindex.||
|m256||Below is a p-chart for a manufacturing process.
a. What is the mean proportion defective? What are the upper and lower control limits?
b. Are there any sample observations that indicate the process is out of control? Which sample numbers are they?
c. Does there seem to be any trend in the process? That is, does the process seem to be getting better, getting worse, or staying thesame?||
|m257||Below is information on the price per share and the dividend for a sample of 30 companies.
a. Calculate the regression equation using selling price based on the annual dividend.
b. Test the significance of the slope.
c. Determine the coefficient of determination. Interpret its value.
d. Determine the correlation coefficient. Can you conclude that it is greater than 0 using the .05 significancelevel?||
|m258||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 amounts in tips per 8-hour shift.
Amount of Tip Number
$0 up to $ 20........ 200
20 up to 50........ 100
50 up to 100........ 75
100 up to 200........ 75
200 or more ........ 50
a. What is the probability of a tip of $200 or more?
b. Are the categories “$0 up to $20,” “$20 up to $50,” 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 $50?
e. What is the probability of a tip of less than $200?||
|m259||Best Electronics Inc. offers a “no hassle” returns policy. The number of items returned per day follows the normal distribution. The mean number of customer returns is 10.3 per day and the standard deviation is 2.25 per day.
a. In what percent of the days are there eight or fewer customers returning items?
b. In what percent of the days are between 12 and 14 customers returning items?
c. Is there any chance of a day with no returns?||
|m260||Bi-lo Appliance Super-Store has outlets in several large metropolitan areas in New England. The general sales manager aired a commercial for a digital camera on selected local TV stations prior to a sale starting on Saturday and ending Sunday. She obtained the information for Saturday–Sunday digital camera sales at the various outlets and paired it with the number of times the advertisement was shown on the local TV stations. The purpose is to find whether there is any relationship between the number of times the advertisement was aired and digital camera sales. The pairings are:
a. What is the dependent variable?
b. Draw a scatter diagram.
c. Determine the correlation coefficient.
d. Interpret these statisticalmeasures.||
|m261||A bin of 50 parts contains five that are defective. A sample of two is selected at random, without replacement.
(a) Determine the probability that both parts in the sample are defective by computing a conditional probability.
(b) Determine the answer to part (a) by using the subset approach that was described in this section.||
|m262||Blueberry Farms Golf and Fish Club of Hilton Head, South Carolina, wants to find monthly seasonal indexes for package play, nonpackage play, and total play. The package play refers to golfers who visit the area as part of a golf package. Typically, the greens fees, cart fees, lodging, maid service, and meals are included as part of a golfing package. The course earns a certain percentage of this total. The nonpackage play includes play by local residents and visitors to the area who wish to play golf. The following data, beginning with July 2010 and ending with June 2013, report the package and nonpackage play by month, as well as the total amount, in thousands of dollars.
Using statistical software:
a. Develop a seasonal index for each month for the package sales. What do you note about the various months?
b. Develop a seasonal index for each month for the nonpackage sales. What do you note about the various months?
c. Develop a seasonal index for each month for the total sales. What do you note about the various months?
d. Compare the indexes for package sales, nonpackage sales, and total sales. Are the busiest months thesame?||
|m263||“Boot time” (the time between the appearance of the Bios screen to the first file that is loaded in Windows) on Eric Mouser’s personal computer follows an exponential distribution with a mean of 27 seconds. What is the probability his “boot” will require:
a. Less than 15 seconds?
b. More than 60 seconds?
c. Between 30 and 45 seconds?
d. What is the point below which only 10% of the boots occur?||