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| m324 | Continuation of Exercise 2-117. Washers are selected from the lot at random, without replacement.
(a) What is the minimum number of washers that need to be selected so that the probability that all the washers are thinner than the target is less than 0.10?
(b) What is the minimum number of washers that need to be selected so that the probability that one or more washers are thicker than the target is at least 0.90? |
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| m325 | Continuation of Exercise 2-63. Suppose three castings are selected at random, without replacement, from the lot of 40. In addition to the definitions of events A and B, let C denote the event that the third casting selected is from the local supplier. Determine:
(a) P (A ∩ B ∩ C)
(b) P (A ∩ B ∩ C’) |
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| m326 | Continuation of Exercise 2-65. Three containers are selected, at random, without replacement, from the batch.
(a) What is the probability that the third one selected is defective given that the first and second one selected were defective?
(b) What is the probability that the third one selected is defective given that the first one selected was defective and the second one selected was okay?
(c) What is the probability that all three are defective? |
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| m327 | Continuation of Exercise 3-108.
(a) What is the probability that you must call four times to obtain the first answer in less than 30 seconds?
(b) What is the mean number of calls until you are answered in less than 30 seconds? |
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| m328 | Continuation of Exercise 3-109.
(a) What is the probability that you must call six times in order for two of your calls to be answered in less than 30 seconds?
(b) What is the mean number of calls to obtain two answers in less than 30 seconds? |
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| m329 | Continuation of Exercise 3-116. Determine the minimum number of assemblies that need to be checked so that the probability of at least one defective assembly exceeds 0.95. |
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| m330 | Continuation of Exercises 3-86 and 3-87.
(a) Calculate the finite population corrections for Exercises 3-86 and 3-87. For which exercise should the binomial approximation to the distribution of X be better?
(b) For Exercise 3-86, calculate P(X = 1) and P(X = 4) assuming that X has a binomial distribution and compare these results to results derived from the hypergeometric distribution.
(c) For Exercise 3-87, calculate P(X = 1) and P(X = 4) assuming that X has a binomial distribution and compare these results to the results derived from the hypergeometric distribution. |
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| m331 | Cooking oil is produced in two main varieties: mono-and polyunsaturated. Two common sources of cooking oil are corn and canola. The following table shows the number of bottles of these oils at a supermarket: |
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| m332 | Cornwall and Hudson, a large retail department store, wants to handle just one brand of high-quality CD player. The list has been narrowed to two brands: Sony and Panasonic. To help make a decision, a panel of 16 audio experts met. A passage using Sony components (labeled A) was played. Then the same passage was played using Panasonic components (labeled B). A “1” in the following table indicates an individual’s preference for the Sony components, a “2” indicates preference for Panasonic, and a 0 signifies no preference.
.:.
Conduct a test of hypothesis at the .10 significance level to determine whether there is a difference in preference between the two brands. |
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| m333 | Counts of the Web pages provided by each of two computer servers in a selected hour of the day are recorded. Let A denote the event that at least 10 pages are provided by server 1 and let B denote the event that at least 20 pages are provided by server 2.
(a) Describe the sample space for the numbers of pages for two servers graphically. Show each of the following events on the sample space graph:
(b) A
(c) B
(d) A ∩ B
(e) A U B) |
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| m334 | CRA CDs Inc. wants the mean lengths of the “cuts” on a CD to be 135 seconds (2 minutes and 15 seconds). This will allow the disk jockeys to have plenty of time for commercials within each 10-minute segment. Assume the distribution of the length of the cuts follows the normal distribution with a population standard deviation of 8 seconds. Suppose we select a sample of 16 cuts from various CDs sold by CRA CDs Inc.
a. What can we say about the shape of the distribution of the sample mean?
b. What is the standard error of the mean?
c. What percent of the sample means will be greater than 140 seconds?
d. What percent of the sample means will be greater than 128 seconds?
e. What percent of the sample means will be greater than 128 but less than 140 seconds? |
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| m335 | A credit card contains 16 digits between 0 and 9. However, only 100 million numbers are valid. If a number is entered randomly, what is the probability that it is a valid number? |
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| m336 | Creek Ratz is a very popular restaurant located along the coast of northern Florida. They serve a variety of steak and seafood dinners. During the summer beach season, they do not take reservations or accept “call ahead” seating. Management of the restaurant is concerned with the time a patron must wait before being seated for dinner. Listed below is the wait time, in minutes, for the 25 tables seated last Saturday night.
a. Explain why the times are a population.
b. Find the mean and median of the times.
c. Find the range and the standard deviation of thetimes. |
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| m337 | Cruise ships of the Royal Viking line report that 80% of their rooms are occupied during September. For a cruise ship having 800 rooms, what is the probability that 665 or more are occupied in September? |
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| m338 | Customers are used to evaluate preliminary product designs. In the past, 95% of highly successful products received good reviews, 60% of moderately successful products received good reviews, and 10% of poor products received good reviews. In addition, 40% of products have been highly successful, 35% have been moderately successful, and 25% have been poor products.
(a) What is the probability that a product attains a good review?
(b) If a new design attains a good review, what is the probability that it will be a highly successful product?
(c) If a product does not attain a good review, what is the probability that it will be a highly successful product? |
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| m339 | Customers at the Bank of Commerce of Idaho Falls, Idaho, default at a rate of .005 on small home-improvement loans. The bank has approved 400 small home-improvement loans.
Assuming the Poisson probability distribution applies to this problem:
a. What is the probability that no homeowners out of the 400 will default?
b. How many of the 400 are expected not to default?
c. What is the probability that three or more homeowners will default on their small home- improvement loans? |
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| m340 | Customers experiencing technical difficulty with their Internet cable hookup may call an 800 number for technical support. It takes the technician between 30 seconds and 10 minutes to resolve the problem. The distribution of this support time follows the uniform distribution.
a. What are the values for a and b in minutes?
b. What is the mean time to resolve the problem? What is the standard deviation of the time?
c. What percent of the problems take more than 5 minutes to resolve?
d. Suppose we wish to find the middle 50% of the problem-solving times. What are the end points of these two times? |
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| m341 | Daniel-James Insurance Company will insure an offshore Mobil Oil production platform against weather losses for one year. The president of Daniel-James estimates the following losses for that platform (in millions of dollars) with the accompanying probabilities:
Amount of Loss Probability
($ millions) of Loss
0 ............. .98
40 ............. .016
300 ............ .004
a. What is the expected amount Daniel-James will have to pay to Mobil in claims?
b. What is the likelihood that Daniel-James will actually lose less than the expected amount?
c. Given that Daniel-James suffers a loss, what is the likelihood that it is for $300 million?
d. Daniel-James has set the annual premium at $2.0 million. Does that seem like a fair premium? Will it cover its risk? |
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| m342 | Dave Christi runs a car wash chain with outlets scattered throughout Chicago. He is concerned that some local managers are giving away free washes to their friends. He decides to collect data on the number of “voided” sales receipts. Of course, some of them are legitimate voids. Would the following data indicate a reasonable number of voids at his facilities: 3, 8, 3, 4, 6, 5, 0, 1, 2, 4? Construct a control chart for this process and comment on whether the process is “in control.” |
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| m343 | Dave’s Automatic Door installs automatic garage door openers. The following list indicates the number of minutes needed to install 10 door openers: 28, 32, 24, 46, 44, 40, 54, 38, 32, and 42.
(a) Range,
(b) Arithmetic mean,
(c) Variance, and
(d) Interpret the statistics. |
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