Answered: What is the probability that a randomly…

Math

Probability

What is the probability that a randomly selected label produced by the company will contain a defective compact disk?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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An automobile manufacturer obtains the microprocessors used to regulate fuel consumption in its automobiles from three microelectronic firms: A, B, and C. The quality-control department of the company has determined that 3% of the microprocessors produced by firm A are defective, 4% of those produced by firm B are defective, and 1.5% of those produced by firm C are defective. Firms A, B, and C supply 35%, 20%, and 45%, respectively, of the microprocessors used by the company. What is the probability that a randomly selected automobile manufactured by the company will have a defective microprocessor?
Avobenzone is one of the active ingredients in several commercially available sunscreens. It can be absorbed into the bloodstream when sunscreen is applied to the skin. The Food and Drug Administration has expressed concern about the safety of absorbing too much avobenzone. Researchers recruited 24 healthy volunteers to investigate avobenzone absorption for four different commercially available sunscreens: two sprays, a lotion, and a cream. Do the types of sunscreens (spray, lotion, and cream) differ in terms of how much avobenzone is absorbed into the blood? Subjects were randomly assigned to one of the four sunscreens, with six subjects for each. Subjects had 2 milligrams of sunscreen per 1 cm? applied to 75% of their body surface area (area outside of normal swimwear) four times per day for four days. The amount of avobenzone absorbed into the bloodstream (in nanograms per milliliter ap-plied, ng/mL) after 150 hours was then measured for each subject. For the purpose of analyzing…
Suppose you are a production manager for a small firm that manufactures GPUs (i.e., video cards) for computers. Your production facility utilizes three identical machines. Quality is binary — each GPU is either defective or it is not defective. Machine 1 produces 40 GPUs per day, and past experience suggests that, on average, 2% of its output will be defective. Machine 2 produces 20 GPUs per day, and past experience suggests that, on average, 3% of its output will be defective. Machine 3 produces 10 GPUs per day, and past experience suggests that 4% of its output will be defective. Any unit of output is not identifiable as having been produced by Machine 1, 2 or 3. (a) Suppose that on March 3, 2022, one GPU is randomly selected from the day’s 70 units of production. That unit is found to be defective. What is the probability that that defective unit was produced by Machine 1? Machine 2? Machine 3? (b) Now suppose that on March 4, 2022, the firm operates only Machine 1. Of its 40 units…
Razor LLC has a data warehouse that is used by several analytics groups. The data warehouse consists of a number of distinct components, including a cloud server (99.999% availability), a database management system server (99.4%), an analytics logic server (94.7%), and, of course, the network infrastructure to the cloud server, which has an availability of 99.9%. What is the overall availability of the system, expressed as a percentage with three digits of precision? For example, enter 91.223, but do not enter a percent symbol, i.e., do not enter 91.223%
Suppose a consumer affairs representative for Mars Incorporated claims that M&M’s plain chocolate candies are mixed such that each large production batch has the following percentages of colored candies: 20% brown, 20% yellow, 10% red, 20% orange, 10% green, and 20% blue. To test this claim, a professor distributed small sample bags of M&M’s to students and had them count the number of candies of each color. The counts of the students were then pooled with the following results. At α=0.05, determine whether there is sufficient evidence to conclude that the percentages are different from what the representative claims. Candy Colors Brown Yellow Red Orange Green Blue Number of candies 190 185 110 168 117 189 Copy Data Step 3 of 4 : Compute the value of the test statistic. Round any intermediate calculations to at least six decimal places, and round your final answer to three decimal places.
This weekend, Premier League officials will be conducting urine tests for all players who are participating in Premier League matches. The tests are being carried out as part of the league's ongoing efforts to combat the use of performance-enhancing drugs and other banned substances. The urine samples will be collected before and after the matches, and will be analysed by a World Anti-Doping Agency (WADA)-accredited laboratory to detect any traces of banned substances in the players' systems. Suppose 3% of the players will use banned substances. Let X be the number of players that officials need to test to find the first case of using banned substances. Let Y be the number of players tested to find 3 such cases. (a) Name the probability distribution and specify the value of any parameter(s) for each of the two random variables X and Y. (b) What is the probability that at least 5 players are to be tested to find the first using-banned-substances case? (c) What is the probability that…
The department of code enforcement of a country government issues permits to general contractors to work on residential projects. For each permit issued, the department inspects the result of the project and gives a "pass" or "fail" rating. A failed project must be re-inspected until it receives a pass rating. The department had been frustrated by the high cost of re-inspection rate and decided to publish the inspection records of all contractors on the web. It was hoped that public access to the records would lower the re-inspection rate. A year after the web access was made public, two samples of records were randomly selected. One sample was selected from the pool of records before web publication and one after. The proportion of projects that passed on the first inspected was noted for each sample. The results are summarized below. No Public Web Access nį = 500, ĝ1 = 0.67 Public Web Access n2 = 100, p2 = 0.80 A test, at a 0.10 level of significance, is to be conducted as to whether…
An insurance company offers four different deductible levels-none,low, medium, and high-for its homeowner's policyholders and threedifferent levels-low, medium, and high-for its automobilepolicyholders. The accompanying table gives proportions for the variouscategories of policyholders who have both types of insurance. Forexample, the proportion of individuals with both low homeowner'sdeductible and low auto deductible is .06 (6% of all such individuals). Homeowner's Auto N L M H LMH .04.07.02 .06.10.03 .05.20.15 .03.10.15 Suppose an individual having both types of policies is randomlyselected.a. What is the probability that the individual has a medium auto deductible and a high homeowner's deductible?b. What is the probability that the individual has a low autodeductible? A low homeowner's deductible?c. What is the probability that the individual is in the samecategory for both auto and homeowner's deductibles?d. Based on your answer in part (c), what is the probability…