| № |
Condition |
free/or 0.5$ |
| m6648 | A corporation has just received new machinery that must be installed and checked before it becomes operational. The accompanying table shows a manager’s probability assessment for the number of days required before the machinery becomes operational.
Let A be the event “it will be more than four days before the machinery becomes operational,” and let B be the event “it will be less than six days before the machinery becomes available.”
a. Find the probability of event A.
b. Find the probability of event B.
c. Find the probability of the complement of event A.
d. Find the probability of the intersection of events A and B.
e. Find the probability of the union of events A and B. |
buy |
| m6649 | A corporation interviews both marketing and finance majors for general management positions. A random sample of 10 marketing majors and an independent random sample of 14 finance majors were subjected to intensive interviewing and testing by a team of the corporation s senior managers. The candidates were then ranked from 1 (most suitable for employment) to 24, as shown in the accompanying table. Test the null hypothesis that, overall, the corporation s senior management has no preference between marketing and finance majors against the alternative that finance majors are preferred. |
buy |
| m6650 | A corporation is considering a new issue of convertible bonds. Management believes that the offer terms will be found attractive by 20% of all its current stockholders.
Suppose that this belief is correct. A random sample of 130 current stockholders is taken.
a. What is the standard error of the sample proportion who find this offer attractive?
b. What is the probability that the sample proportion is more than 0.15?
c. What is the probability that the sample proportion is between 0.18 and 0.22?
d. Suppose that a sample of 500 current stockholders had been taken. Without doing the calculations, state whether the probabilities in parts (b) and (c) would have been higher, lower, or the same as those found. |
buy |
| m6651 | A corporation is trying to decide which of three makes of automobile to order for its fleet-domestic, Japanese, or European. Five cars of each type were ordered, and, after 10,000 miles of driving, the operating cost per mile of each was assessed. The accompanying results in cents per mile were obtained.
a. Prepare the analysis of variance table for these data.
b. Test the null hypothesis that the population mean operating costs per mile are the same for these three types of car.
c. Compute the minimum significant difference and indicate which subgroups have different means. |
buy |
| m6652 | A corporation receives 120 applications for positions from recent college graduates in business. Assuming that these applicants can be viewed as a random sample of all such graduates, what is the probability that between 35% and 45% of them are women if 40% of all recent college graduates in business are women? |
buy |
| m6653 | A corporation receives a particular part in shipments of 100. Research indicated the probabilities shown in the accompanying table for numbers of defective parts in a shipment.
a. What is the probability that there will be fewer than three defective parts in a shipment?
b. What is the probability that there will be more than one defective part in a shipment?
c. The five probabilities in the table sum to 1. Why must this be so? |
buy |
| m6654 | A corporation regularly takes deliveries of a particular sensitive part from three subcontractors. It found that the proportion of parts that are good or defective from the total received were as shown in the following table:
a. If a part is chosen randomly from all those received, what is the probability that it is defective?
b. If a part is chosen randomly from all those received, what is the probability it is from subcontractor B?
c. What is the probability that a part from subcontractor B is defective?
d. What is the probability that a randomly chosen defective part is from subcontractor B?
e. Is the quality of a part independent of the source of supply?
f. In terms of quality, which of the three subcontractors is most reliable? |
buy |
| m6655 | A corporation takes delivery of some new machinery that must be installed and checked before it becomes available to use. The corporation is sure that it will take no more than 7 days for this installation and check to take place. Let A be the event "it will be more than 4 days before the machinery becomes available" and B be the event "it will be less than 6 days before the machinery becomes available."
a. Describe the event that is the complement of event A.
b. Describe the event that is the intersection of events A and B.
c. Describe the event that is the union of events A and B.
d. Are events A and B mutually exclusive?
e. Are events A and B collectively exhaustive?
f. Show that (A ∩ B) ( (A ∩ B) = B.
g. Show that A ( (A ∩ B) = A ( B. |
buy |
| m6656 | A corporation was concerned with the basic educational skills of its workers and decided to offer a selected group of them separate classes in reading and practical mathematics. Of these workers, 40% signed up for the reading classes and 50% for the practical mathematics classes. Of those signing up for the reading classes 30% signed up for the mathematics classes.
a. What is the probability that a randomly selected worker signed up for both classes?
b. What is the probability that a randomly selected worker who signed up for the mathematics classes also signed up for the reading classes?
c. What is the probability that a randomly chosen worker signed up for at least one of these two classes?
d. Are the events "signs up for the reading classes" and "signs up for the mathematics classes" statistically independent? |
buy |
| m6657 | A country club wants to poll a random sample of its 320 members to estimate the proportion likely to attend an early-season function. The number of sample observations should be sufficiently large to ensure that a 99% confidence interval for the population extends at most 0.05 on each side of the sample proportion. How large of a sample is necessary? |
buy |
| m6658 | A customer service center in India receives, on average, 4.2 telephone calls per minute. If the distribution of calls is Poisson, what is the probability of receiving at least 3 calls during a particular minute? |
buy |
| m6659 | A dean has found that 62% of entering freshmen and 78% of community college transfers eventually graduate. Of all entering students, 73% are entering freshmen and the remainder are community college transfers.
a. What is the probability that a randomly chosen entering student is an entering freshman who will eventually graduate?
b. Find the probability that a randomly chosen entering student will eventually graduate.
c. What is the probability that a randomly chosen entering student either is an entering freshman or will eventually graduate (or both)?
d. Are the events "eventually graduates" and "enters as community college transfer" statistically independent? |
buy |
| m6660 | A department store manager has monitored the number of complaints received per week about poor service. The probabilities for numbers of complaints in a week, established by this review, are shown in the following table. Let A be the event “there will be at least one complaint in a week” and B the event “there will be fewer than ten complaints in a week.”
a. Find the probability of A.
b. Find the probability of B.
c. Find the probability of the complement of A.
d. Find the probability of the union of A and B.
e. Find the probability of the intersection of A and B.
f. Are A and B mutually exclusive?
g. Are A and B collectively exhaustive? |
buy |
| m6661 | A department-store chain randomly sampled 10 stores in a state. After a review of sales records, it was found that, compared with the same period last year, the following percentage increases in dollar sales had been achieved over the Christmas period this year:
10.2 3.1 5.9 7.0 3.7 2.9 6.8 7.3 8.2 4.3
a. Calculate the mean percentage increase in dollar sales.
b. Calculate the median. |
buy |
| m6662 | A department-store manager is interested in the number of complaints received by the customer-service department about the quality of electrical products sold by the store. Records over a 5-week period show the following number of complaints for each week:
13 15 8 16 8
a. Compute the mean number of weekly complaints.
b. Calculate the median number of weekly complaints.
c. Find the mode. |
buy |
| m6663 | A dependent random sample from two normally distributed populations gives the following results:
n = 15 d-bar = 25.4 sd = 2.8
a. Find the 95% confidence interval for the difference between the means of the two populations.
b. Find the margin of error for a 95% confidence interval for the difference between the means of the two populations. |
buy |
| m6664 | A dependent variable is regressed on K independent variables, using n sets of sample observations. We denote SSE as the error sum of squares and R2 as the coefficient of determination for this estimated regression. We want to test the null hypothesis that K1 of these independent variables, taken together, do not linearly affect the dependent variable, given that the other (K – K1) independent variables are also to be used. Suppose that the regression is reestimated with the K1 independent variables of interest excluded. Let SSE* denote the error sum of squares and R*2, the coefficient of determination for this regression. Show that the statistic for testing our null hypothesis, introduced in Section 12.5, can be expressed as follows: |
buy |
| m6665 | A dependent variable is regressed on two independent variables. It is possible that the hypotheses H0: β1 = 0 and H0: β2 = 0 cannot be rejected at low significance levels, yet the hypothesis H0: β1 = β2 = 0 can be rejected at a very low significance level. In what circumstances might this result arise? |
buy |
| m6666 | A diet soda manufacturer wants to compare the effects on sales of three can colors-red, yellow, and blue. Four regions are selected for the test, and three stores are randomly chosen from each region, each to display one color of cans. The accompanying table shows sales (in tens of cans) at the end of the experimental period.
a. Prepare the appropriate analysis of variance table.
b. Test the null hypothesis that population mean sales are the same for each can color. |
buy |
| m6667 | A drug company produces pills containing an active ingredient. The company is concerned about the mean weight of this ingredient per pill, but it also requires that the variance (in squared milligrams) be no more than 1.5. A random sample of 20 pills is selected, and the sample variance is found to be 2.05. How likely is it that a sample variance this high or higher would be found if the population variance is, in fact, 1.5? Assume that the population distribution is normal. |
buy |