A.2 According to Chemical Engineering Progress (November 1990), approximately 30% of all pipework failures in chemical plants are caused by operator error. (a) What is the probability that out of the next 20 pipework failures at least 10 are due to operator error? (b) What is the probability that no more than 4 out of 20 such failures are due to operator error? (c) Suppose, for a particular plant, that out of the random sample of 20 such failures, exactly 5 are due to operator error. Do you feel that the 30% figure stated above applies to this plant? Comment.

A.2 According to Chemical Engineering Progress (November 1990), approximately 30% of all pipework failures in chemical plants are caused by operator error. (a) What is the probability that out of the next 20 pipework failures at least 10 are due to operator error? (b) What is the probability that no more than 4 out of 20 such failures are due to operator error? (c) Suppose, for a particular plant, that out of the random sample of 20 such failures, exactly 5 are due to operator error. Do you feel that the 30% figure stated above applies to this plant? Comment.

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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When functioning correctly, a machine produces switches with a 0.8% defective rate. Find the probability that a batch of 1,000 switches contains 14 or more defective switches (assuming that the machine functions correctly, i.e., the population defective rate is 0.8%). Suppose a batch of 1,000 switches were inspected when completed, and 14 defective switches were found. Based on your answer to part a, does this sample imply that the machine needs adjustment? Explain your answer.
A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 22 tablets, then accept the whole batch if there is only one or none that doesn't meet the required specifications. If a particular shipment of thousands of aspirin tablets actually has a 6% rate of defects, what is the probability that this whole shipment will be accepted? ... The probability that this whole shipment will be accepted is (Round to three decimal places as needed.)
When a scientist conducted a genetics experiments with peas, one sample of offspring consisted of 927 peas, with 723 of them having red flowers. If we assume, as the scientist did, that under these circumstances, there is a 3/4 probability that a pea will have a red flower, we would expect that 695.25 (or about 695) of the peas would have red flowers, so the result of 723 peas with red flowers is more than expected. a. If the scientist's assumed probability is correct, find the probability of getting 723 or more peas with red flowers. b. Is 723 peas with red flowers significantly high? c. What do these results suggest about the scientist's assumption that 3/4 of peas will have red flowers?
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A manufacturing company regularly conducts quality control checks at specified periods on the products it manufactures. Historically, the failure rate for LED light bulbs that the company manufactures is 2%. Suppose a random sample of10 LED light bulbs is selected. Complete parts (a) through (d) below. (A) What is the probability that none of the LED light bulbs are defective? (B)What is the probability that exactly one of the LED light bulbs is defective? (C)What is the probability that three or fewer of the LED light bulbs are defective (D) What is the probability that four or more of the LED light bulbs are defective?
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(a) Suppose it is known that 5% of adults who take a certain medication experience side effects. If a random sample of 16 adults is drawn, what is E (1) (11) the expected number of adults are not having side effects? the probability that more than 14 adults are not having side effects? the probability that 9 or 12 adults are not having side effects?