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| m548 | In a chemical plant, 24 holding tanks are used for final product storage. Four tanks are selected at random and without replacement. Suppose that six of the tanks contain material in which the viscosity exceeds the customer requirements.
(a) What is the probability that exactly one tank in the sample contains high viscosity material?
(b) What is the probability that at least one tank in the sample contains high viscosity material?
(c) In addition to the six tanks with high viscosity levels, four different tanks contain material with high impurities. What is the probability that exactly one tank in the sample contains high viscosity material and exactly one tank in the sample contains material with high impurities? |
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| m549 | In circuit testing of printed circuit boards, each board either fails or does not fail the test. A board that fails the test is then checked further to determine which one of five defect types is the primary failure mode. Represent the sample space for this experiment. |
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| m550 | In a clinical study, volunteers are tested for a gene that has been found to increase the risk for a disease. The probability that a person carries the gene is 0.1.
(a) What is the probability 4 or more people will have to be tested before 2 with the gene are detected?
(b) How many people are expected to be tested before 2 with the gene are detected? |
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| m552 | In each of the following cases, indicate whether classical, empirical, or subjective probability is used.
a. A baseball player gets a hit in 30 out of 100 times at bat. The probability is .3 that he gets a hit in his next at bat.
b. A seven-member committee of students is formed to study environmental issues. What is the likelihood that any one of the seven is randomly chosen as the spokesperson?
c. You purchase 1 of 5 million tickets sold for Lotto Canada. What is the likelihood you will win the $1 million jackpot?
d. The probability of an earthquake in northern California in the next 10 years above 5.0 on the Richter Scale is .80. |
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| m553 | In Exercise 3-66, recall that 20 parts are checked each hour and that X denotes the number of parts in the sample of 20 that require rework.
(a) If the percentage of parts that require rework remains at 1%, what is the probability that hour 10 is the first sample at which X exceeds 1?
(b) If the rework percentage increases to 4%, what is the probability that hour 10 is the first sample at which X exceeds 1?
(c) If the rework percentage increases to 4%, what is the expected number of hours until X exceeds 1? |
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| m554 | In Exercise 3-70, recall that a particularly long traffic light on your morning commute is green 20% of the time that you approach it. Assume that each morning represents an independent trial.
(a) What is the probability that the first morning that the light is green is the fourth morning that you approach it?
(b) What is the probability that the light is not green for 10 consecutive mornings? |
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| m555 | In an injection-molding operation, the length and width, denoted as X and Y, respectively, of each molded part are evaluated. Let
A denote the event of 48 = X = 52 centimeters
B denote the event of 9 = Y = 11 centimeters
C denote the event that a critical length meets customer requirements.
Construct a Venn diagram that includes these events. Shade the areas that represent the following:
(a) A
(b) A ∩ B
(c) A’ U B
(d) A U B
(e) If these events were mutually exclusive, how successful would this production operation be? Would the process produce parts with X _ 50 centimeters and Y _ 10 centimeters? |
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| m556 | In item such as an increase in taxes, recall of elected officials, or an expansion of public services can be placed on the ballot if a required number of valid signatures are collected on the petition. Unfortunately, many people will sign the petition even though they are not registered to vote in that particular district, or they will sign the petition more than once.
Sara Ferguson, the elections auditor in Venango County, must certify the validity of these signatures after the petition is officially presented. Not surprisingly, her staff is overloaded, so she is considering using statistical methods to validate the pages of 200 signatures, instead of validating each individual signature. At a recent professional meeting, she found that, in some communities in the state, election officials were checking only five signatures on each page and rejecting the entire page if two or more signatures were invalid. Some people are concerned that five may not be enough to make a good decision. They suggest that you should check 10 signatures and reject the page if 3 or more are invalid.
In order to investigate these methods, Sara asks her staff to pull the results from the last election and sample 30 pages. It happens that the staff selected 14 pages from the Avondale district, 9 pages from the Midway district, and 7 pages from the Kingston district. Each page had 200 signatures, and the data below show the number of invalid signatures on each.
Use the data to evaluate Sara’s t |
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| m557 | In June, an investor purchased 300 shares of Oracle (an information technology company) stock at $20 per share. In August, she purchased an additional 400 shares at $25 per share. In November, she purchased an additional 400 shares, but the stock declined to $23 per share. What is the weighted mean price per share? |
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| m558 | In a manufacturing operation, a part is produced by machining, polishing, and painting. If there are three machine tools, four polishing tools, and three painting tools, how many different routings (consisting of machining, followed by polishing, and followed by painting) for a part are possible? |
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| m559 | In a manufacturing process that laminates several ceramic layers, 1% of the assemblies are defective. Assume that the assemblies are independent.
(a) What is the mean number of assemblies that need to be checked to obtain five defective assemblies?
(b) What is the standard deviation of the number of assemblies that need to be checked to obtain five defective assemblies? |
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| m560 | In recent times, with mortgage rates at low levels, financial institutions have had to provide more customer convenience. One of the innovations offered by Coastal National Bank and Trust is online entry of mortgage applications. Listed below are the times, in minutes, for eight customers to complete the application process for a 15-year fixed-rate mortgage and the times for nine customers to complete an application for a 30-year fixed-rate mortgage.
15 years, fixed rate ...... 41, 36, 42, 39, 36, 48, 49, 38
30 years, fixed rate ...... 21, 27, 36, 20, 19, 21, 39, 24, 22
At the .05 significance level, is it reasonable to conclude that it takes less time for those customers applying for the 30-year fixed-rate mortgage? Do not assume the distribution times follow a normal distribution for either group. |
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| m561 | In recent years, due to low interest rates, many homeowners refinanced their home mort-gages. Linda Lahey is a mortgage officer at Down River Federal Savings and Loan. Below is the amount refinanced for 20 loans she processed last week. The data are reported in thousands of dollars and arranged from smallest to largest.
a. Find the median, first quartile, and third quartile.
b. Find the 26th and 83rd percentiles.
c. Draw a box plot of thedata. |
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| m562 | In a semiconductor manufacturing process, three wafers from a lot are tested. Each wafer is classified as pass or fail. Assume that the probability that a wafer passes the test is 0.8 and that wafers are independent. Determine the probability mass function of the number of wafers from a lot that pass the test. |
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| m563 | In a sheet metal operation, three notches and four bends are required. If the operations can be done in any order, how many different ways of completing the manufacturing are possible? |
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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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