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| m664 | A lot of 75 washers contains 5 in which the variability in thickness around the circumference of the washer is unacceptable. A sample of 10 washers is selected at random, without replacement.
(a) What is the probability that none of the unacceptable washers is in the sample?
(b) What is the probability that at least one unacceptable washer is in the sample?
(c) What is the probability that exactly one unacceptable washer is in the sample?
(d) What is the mean number of unacceptable washers in the sample? |
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| m665 | m – n/5, when m = 16 and n = |
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| m666 | A machine tool is idle 15% of the time. You request immediate use of the tool on five different occasions during the year. Assume that your requests represent independent events.
(a) What is the probability that the tool is idle at the time of all of your requests?
(b) What is the probability that the machine is idle at the time of exactly four of your requests?
(c) What is the probability that the tool is idle at the time of at least three of your requests? |
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| m667 | Magnetic tape is slit into half-inch widths that are wound into cartridges. A slitter assembly contains 48 blades. Five blades are selected at random and evaluated each day for sharpness. If any dull blade is found, the assembly is replaced with a newly sharpened set of blades.
(a) If 10 of the blades in an assembly are dull, what is the probability that the assembly is replaced the first day it is evaluated?
(b) If 10 of the blades in an assembly are dull, what is the probability that the assembly is not replaced until the third day of evaluation? [Hint: Assume the daily decisions are independent, and use the geometric distribution.]
(c) Suppose on the first day of evaluation, two of the blades are dull, on the second day of evaluation six are dull, and on the third day of evaluation, ten are dull. What is the probability that the assembly is not replaced until the third day of evaluation? [Hint: Assume the daily decisions are independent. However, the probability of replacement changes every day.] |
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| m668 | A maintenance firm has gathered the following information regarding the failure mechanisms for air conditioning systems: |
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| m669 | A manufacturer of a consumer electronics product expects 2% of units to fail during the warranty period. A sample of 500 independent units is tracked for warranty performance.
(a) What is the probability that none fails during the warranty period?
(b) What is the expected number of failures during the warranty period?
(c) What is the probability that more than two units fail during the warranty period? |
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| m670 | A manufacturer of front lights for automobiles tests lamps under a high humidity, high temperature environment using intensity and useful life as the responses of interest. The following table shows the performance of 130 lamps: |
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| m671 | A manufacturer stocks components obtained from a supplier. Suppose that 2% of the components are defective and that the defective components occur independently. How many components must the manufacturer have in stock so that the probability that 100 orders can be completed without reordering components is at least 0.95?v |
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| m672 | A manufacturing operations consists of 10 operations. However, five machining operations must be completed before any of the remaining five assembly operations can begin. Within each set of five, operations can be completed in any order. How many different production sequences are possible? |
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| m673 | A manufacturing process consists of 10 operations that can be completed in any order. How many different production sequences are possible? |
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| m674 | Many grocery stores and large retailers such as Walmart and Kmart have installed self-checkout systems so shoppers can scan their own items and cash out themselves. How do customers like this service and how often do they use it? Listed below is the number of customers using the service for a sample of 15 days at a Walmart location.
Is it reasonable to conclude that the mean number of customers using the self-checkout system is more than 100 per day? Use the .05 significancelevel. |
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| m675 | Many new stockbrokers resist giving presentations to bankers and certain other groups. Sensing this lack of self-confidence, management arranged to have a confidence-building seminar for a sample of new stockbrokers and enlisted Career Boosters for a three-week course. Before the first session, Career Boosters measured the level of confidence of each participant. It was measured again after the three-week seminar. The before and after levels of self-confidence for the 14 in the course are shown below. Self-confidence was classified as being either negative low, high, or very high.
The purpose of this study is to find whether Career Boosters was effective in raising the self-confidence of the new stockbrokers. That is, was the level of self-confidence higher after the seminar than before it? Use the .05 significance level.
a. State the null and alternate hypotheses.
b. Using the .05 level of significance, state the decision rule—either in words or in chart form.
c. Draw conclusions about the seminar offered by CareerBoosters. |
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| m676 | Many regions along the coast in North and South Carolina and Georgia have experienced rapid population growth over the last 10 years. It is expected that the growth will continue over the next 10 years. This has motivated many of the large grocery store chains to build new stores in the region. The Kelley’s Super Grocery Stores Inc. chain is no exception. The director of planning for Kelley’s Super Grocery Stores wants to study adding more stores in this region. He believes there are two main factors that indicate the amount families spend on groceries. The first is their income and the other is the number of people in the family. The director gathered the following sample information.
Food and income are reported in thousands of dollars per year, and the variable size refers to the number of people in the household.
a. Develop a correlation matrix. Do you see any problems with multicollinearity?
b. Determine the regression equation. Discuss the regression equation. How much does an additional family member add to the amount spent on food?
c. What is the value of R2? Can we conclude that this value is greater than 0?
d. Would you consider deleting either of the independent variables?
e. Plot the residuals in a histogram. Is there any problem with the normality assumption?
f. Plot the fitted values against the residuals. Does this plot indicate any problems withhomoscedasticity? |
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| m677 | Many retail stores offer their own credit cards. At the time of the credit application, the customer is given a 10% discount on the purchase. The time required for the credit application process follows a uniform distribution with the times ranging from 4 minutes to 10 minutes.
a. What is the mean time for the application process?
b. What is the standard deviation of the process time?
c. What is the likelihood a particular application will take less than 6 minutes?
d. What is the likelihood an application will take more than 5 minutes? |
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| m678 | Marketing estimates that a new instrument for the analysis of soil samples will be very successful, moderately successful, or unsuccessful, with probabilities 0.3, 0.6, and 0.1, respectively. The yearly revenue associated with a very successful, moderately successful, or unsuccessful product is $10 million, $5 million, and $1 million, respectively. Let the random variable X denote the yearly revenue of the product. Determine the probability mass function of X. |
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| m679 | Martin Motors has in stock three cars of the same make and model. The Sales Manager 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.
Using the .05 level of significance:
a. Is there a difference among types of gasoline?
b. Is there a difference in thecars? |
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| m680 | Mary Jo Fitzpatrick is the vice president for Nursing Services at St. Luke’s Memorial Hospital. Recently she noticed in the job postings for nurses that those that are unionized seem to offer higher wages. She decided to investigate and gathered the following information.
Would it be reasonable for her to conclude that union nurses earn more? Use the .02 significance level. What is thep-value? |
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| m681 | McGivern Jewelers is located in the Levis Square Mall just south of Toledo, Ohio. Recently it ran an advertisement in the local newspaper reporting the shape, size, price, and cut grade for 33 of its diamonds currently in stock. The information is reported below.
a. Develop a box plot of the variable price and comment on the result. Are there any outliers? What is the median price? What are the values of the first and the third quartiles?
b. Develop a box plot of the variable size and comment on the result. Are there any outliers? What is the median price? What are the values of the first and the third quartiles?
c. Develop a scatter diagram between the variables price and size. Be sure to put price on the vertical axis and size on the horizontal axis. Does there seem to be an association between the two variables? Is the association direct or indirect? Does any point seem to be different from the others?
d. Develop a contingency table for the variables shape and cut grade. What is the most common cut grade? What is the most common shape? What is the most common combination of cut grade andshape? |
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| m682 | Merrill Lynch recently completed a study regarding the size of online investment portfolios (stocks, bonds, mutual funds, and certificates of deposit) for a sample of clients in the 40 up to 50 years old age group. Listed following is the value of all the investments in thousands of dollars for the 70 participants in the study.
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a. Organize the data into a frequency distribution. How many classes would you suggest? What value would you suggest for a class interval?
b. Draw a histogram. Interpret your result. |
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| m683 | A message can follow different paths through servers on a network. The senders message can go to one of five servers for the first step, each of them can send to five servers at the second step, each of which can send to four servers at the third step, and then the message goes to the recipients server.
(a) How many paths are possible?
(b) If all paths are equally likely, what is the probability that a message passes through the first of four servers at the third step? |
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