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| m564 | In a test of a printed circuit board using a random test pattern, an array of 10 bits is equally likely to be 0 or 1.
Assume the bits are independent.
(a) What is the probability that all bits are 1s?
(b) What is the probability that all bits are 0s?
(c) What is the probability that exactly five bits are 1s and five bits are 0s? |
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| m565 | In the Department of Education at UR University, student records suggest that the population of students spends an average of 5.5 hours per week playing organized sports. The population’s standard deviation is 2.2 hours per week. Based on a sample of 121 students, Healthy Lifestyles Incorporated (HLI) would like to apply the central limit theorem to make various estimates.
a. Compute the standard error of the sample mean.
b. What is the chance HLI will find a sample mean between 5 and 6 hours?
c. Calculate the probability that the sample mean will be between 5.3 and 5.7 hours.
d. How strange would it be to obtain a sample mean greater than 6.5 hours? |
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| m566 | In the design of an electromechanical product, seven different components are to be stacked into a cylindrical casing that holds 12 components in a manner that minimizes the impact of shocks. One end of the casing is designated as the bottom and the other end is the top.
(a) How many different designs are possible?
(b) If the seven components are all identical, how many different designs are possible?
(c) If the seven components consist of three of one type of component and four of another type, how many different designs are possible? (More difficult) |
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| m567 | In the final inspection of electronic power supplies, three types of nonconformities might occur: functional, minor, or cosmetic. Power supplies that are defective are further classified as to type of nonconformity. |
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| m568 | In the laboratory analysis of samples from a chemical process, five samples from the process are analyzed daily. In addition, a control sample is analyzed two times each day to check the calibration of the laboratory instruments.
(a) How many different sequences of process and control samples are possible each day? Assume that the five process samples are considered identical and that the two control samples are considered identical.
(b) How many different sequences of process and control samples are possible if we consider the five process samples to be different and the two control samples to be identical?
(c) For the same situation as part (b), how many sequences are possible if the first test of each day must be a control sample? |
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| m569 | In the law firm Tybo and Associates, there are six partners. Listed next is the number of cases each partner actually tried in court last month.
Partner Number of Cases
Ruud........ 3
Wu........ 6
Sass........ 3
Flores........ 3
Wilhelms........ 0
Schueller........ 1
a. How many different samples of size 3 are possible?
b. List all possible samples of size 3, and compute the mean number of cases in each sample.
c. Compare the mean of the distribution of sample means to the population mean.
d. On a chart similar to Chart 8–2, compare the dispersion in the population with that of the sample means. |
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| m570 | In the layout of a printed circuit board for an electronic product, there are 12 different locations that can accommodate chips.
(a) If five different types of chips are to be placed on the board, how many different layouts are possible?
(b) If the five chips that are placed on the board are of the same type, how many different layouts are possible? |
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| m571 | In the manufacturing of a chemical adhesive, 3% of all batches have raw materials from two different lots. This occurs when holding tanks are replenished and the remaining portion of a lot is insufficient to fill the tanks. Only 5% of batches with material from a single lot require reprocessing. However, the viscosity of batches consisting of two or more lots of material is more difficult to control, and 40% of such batches require additional processing to achieve the required viscosity. Let A denote the event that a batch is formed from two different lots, and let B denote the event that a lot requires additional processing. Determine the following probabilities:
(a) P (A)
(b) P (A’)
(c) P (B|A)
(d) P (B|A’)
(e) P (A ∩ B)
(f) p (A ∩ B’)
(g) P (B) |
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| m572 | In the manufacturing of digital recording tape, each of 24 tracks is classified as containing or not containing one or more bits in error. |
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| m573 | In the United States, the industrial revolution of the early 20th century changed farming by making it more efficient. For example, in 1910 U.S. farms used 24.2 million horses and mules and only about 1,000 tractors. By 1960, 4.6 million tractors were used and only 3.2 million horses and mules. An outcome of making farming more efficient is the reduction of the number of farms from over 6 million in 1920 to about 2.2 million farms today. Listed below is the number of farms, in thousands, for each of the 50 states. Summarize the data and write a paragraph that describes your findings. |
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| m574 | In a voice communication system with 50 lines, the random variable is the number of lines in use at a particular time. |
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| m575 | Incoming calls to a customer service center are classified as complaints (75% of call) or requests for information (25% of calls). Of the complaints, 40% deal with computer equipment that does not respond and 57% deal with incomplete software installation; and in the remaining 3% of complaints the user has improperly followed the installation instructions. The requests for information are evenly divided on technical questions (50%) and requests to purchase more products (50%).
(a) What is the probability that an incoming call to the customer service center will be from a customer who has not followed installation instructions properly?
(b) Find the probability that an incoming call is a request for purchasing more products. |
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| m576 | Industry standards suggest that 10% of new vehicles require warranty service within the first year. Jones Nissan in Sumter, South Carolina, sold 12 Nissans yesterday.
a. What is the probability that none of these vehicles requires warranty service?
b. What is the probability exactly one of these vehicles requires warranty service?
c. Determine the probability that exactly two of these vehicles require warranty service.
d. Compute the mean and standard deviation of this probability distribution. |
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| m577 | Information from the American Institute of Insurance indicates the mean amount of life insurance per household in the United States is $110,000. This distribution follows the normal distribution with a standard deviation of $40,000.
a. If we select a random sample of 50 households, what is the standard error of the mean?
b. What is the expected shape of the distribution of the sample mean?
c. What is the likelihood of selecting a sample with a mean of at least $112,000?
d. What is the likelihood of selecting a sample with a mean of more than $100,000?
e. Find the likelihood of selecting a sample with a mean of more than $100,000 but less than $112,000. |
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| m578 | An injection-molded part is equally likely to be obtained from any one of the eight cavities on a mold.
(a) What is the sample space?
(b) What is the probability a part is from cavity 1 or 2?
(c) What is the probability that a part is neither from cavity 3 nor 4? |
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| m579 | An inspector working for a manufacturing company has a 99% chance of correctly identifying defective items and a 0.5% chance of incorrectly classifying a good item as defective. The company has evidence that its line produces 0.9% of nonconforming items.
(a) What is the probability that an item selected for inspection is classified as defective?
(b) If an item selected at random is classified as nondefective, what is the probability that it is indeed good? |
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| m580 | An installation technician for a specialized communication system is dispatched to a city only when three or more orders have been placed. Suppose orders follow a Poisson distribution with a mean of 0.25 per week for a city with a population of 100,000 and suppose your city contains a population of 800,000. (a) What is the probability that a technician is required after a one-week period? (b) If you are the first one in the city to place an order, what is the probability that you have to wait more than two weeks from the time you place your order until a technician is dispatched? |
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| m581 | Inter State Moving and Storage Company is setting up a control chart to monitor the proportion of residential moves that result in written complaints due to late delivery, lost items, or damaged items. A sample of 50 moves is selected for each of the last 12 months. The number of written complaints in each sample is 8, 7, 4, 8, 2, 7, 11, 6, 7, 6, 8, and 12.
a. Design a p-chart and label the mean proportion defective, UCL, and LCL.
b. Plot the proportion of written complaints in the last 12 months.
c. Interpret the chart. Does it appear that the number of complaints is out of control for any of the months? |
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| m582 | Is there a difference (in feet) of the length of suspension bridges in the northeast, southeast, and far west parts of the United States? The following table shows the lengths of seven bridges in the northeast, nine bridges in the southeast, and eight bridges in the far west. Conduct an appropriate test of hypothesis on the following data. Do not assume the bridge lengths follow a normal probability distribution. Use the .05 significancelevel. |
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| m583 | Is there a difference in the annual divorce rates in predominantly rural counties among three geographic regions, namely, the Southwest, the Southeast, and the Northwest? Test at the .05 level. Annual divorce rates per 1,000 population for five randomly selected counties in the Southwest, six counties in the Southeast, and 5 counties in the Northwest are:
Southwest: ........ 5.9, 6.2, 7.9, 8.6, 4.6
Southeast: ....... 5.0, 6.4, 7.3, 6.2, 8.1, 5.1
Northwest: ........ 6.7, 6.2, 4.9, 8.0, 5.5 |
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