Question 3Consider the set of Bernoulli trials where three items are selected at random from a manufacturingprocess, inspected, and classified as defective or nondefective. The eight possible outcomes and thecorresponding values of X areOutcome NNN NDN NND DNN NDD DND DDN DDDI01112223Since the items are selected independently and we assume that the process produces 25% defectives.(a) Find the probability distribution of X (Hint: You have to create a table.).(b) Find μ2x+3.

Answered: Image /qna-images/answer/216cab60-6175-4172-a174-7245e44a5697.jpg

Answered: Consider the set of Bernoulli trials…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The 2010 census shows that 6% of the American population are at least 75 years of age. To test a random digit dialing device, you use the device to call randomly chosen residential telephones in your county. Of the 150 members of the households contacted, 4% are 75 years or older. Assume that your county's population is similar to the American population in age distribution. What is the probability that a random sample of 150 respondents would contain less than 4% of individuals at least 75 years of age?
Oxygen demand is a term biologists use to describe the oxygen needed by fish and other aquatic organisms for survival. The Environmental Protection Agency conducted a study of a wetland area. In this wetland environment, the mean oxygen demand was μ = 9.1 mg/L with 95% of the data ranging from 6.7 mg/L to 11.5 mg/L. Let x be a random variable that represents oxygen demand in this wetland environment. Assume x has a probability distribution that is approximately normal. QUESTION: (b) An oxygen demand below 8 indicates that some organisms in the wetland environment may be dying. What is the probability that the oxygen demand will fall below 8 mg/L? (Round your answer to four decimal places.)
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Suppose that 10% of all homeowners in an earthquake-prone area of California are insured against earthquake damage. Four homeowners are selected at random. Define the random variable x as the number among the four who have earthquake insurance. (a)Find the probability distribution of x. (Hint: Let S denote a homeowner who has insurance and F one who does not. Then one possible outcome is SFSS, with probability (.1)(.9)(.1)(.1) and associated x value of 3. There are 15 other outcomes.) Value of x probability 0 1 2 3 4 (c)What is the probability that at least two of the four selected homeowners have earthquake insurance? P (at least 2 of the 4 have earthquake insurance) =
Oxygen demand is a term biologists use to describe the oxygen needed by fish and other aquatic organisms for survival. The Environmental Protection Agency conducted a study of a wetland area. In this wetland environment, the mean oxygen demand was μ = 9.9 mg/L with 95% of the data ranging from 7.3 mg/L to 12.5 mg/L. Let x be a random variable that represents oxygen demand in this wetland environment. Assume x has a probability distribution that is approximately normal. (a) Use the 95% data range to estimate the standard deviation for oxygen demand.
A random experiment was run 23 times with groups of 24 mice. Each time the experiment was run, 4 mice were initially infected with a disease; the remaining mice were susceptible to contracting the disease. After one day, they measured the number of number of newly infected mice (not including those originally infected). They found the following frequency table: Newly infected mice Newly infected mice 4 5 6 7 8 9 10 11 Frequency 1 2 2 6 5 4 2 1 Determine the expected probability of transmission for this particular variant of disease. Round your answer to three decimal places.
Two candidates are running for president: John Democrat and Joe Republican. A recent survey concluded that John Democrat had a probability of 0.55 to win the election. One thousand people are interviewed at random about whom they would vote for. A random variable X is defined as the number of people who said they would vote for Joe Republican. Find the expected value of the random variable
A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 52 tablets, then accept the whole batch if there is only one or none that doesn't meet the required specifications. If one shipment of 4000 aspirin tablets actually has a 5% rate of defects, what is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will many be rejected? The probability that this whole shipment will be accepted is ______ (Round to four decimal places as needed.) The company will accept ____% of the shipments and will reject ____% of the shipments, so______________ (many of the shipments will be rejected or almost all of the shipments will be accepted. (Round to two decimal places as needed.)
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(b) In a semiconductor company, the failures of the component are very high due to quality control issues. To make sure this problem is no longer an issue, the quality team has set their acceptance criterion for a production line not to have more than 4 defectives in every 30 samples. By giving the production yield (goods) as low as 20%, determine the ( acceptance probability of this production line set by quality team. It was found
A doctor is interested in the proportion of patients which live at least 5 years after being diagnosed with stage 4 breast cancer. He randomly selects 138 patients diagnosed with stage 4 breast cancer and follows them for 5 years. Suppose the true 5 year survival rate for stage 4 breast cancer is 38%. 1. How are the collection of all sample proportions of samples of size 138 distributed? NO 2. What is the probability that fewer than 34% of the patients studied survived for at least 5 years? o List the z-scores needed to calculate the result. If there is more than one z-score, separate the values with a comma. o There is a survived for at least 5 years. 3. What is the probability that more than 45% of the patients studied survived for at least 5 years? chance that fewer than 34% of the patients studied o List the z-scores needed to calculate the result. If there is more than one z-score, separate the values with a comma. O There is a survived for at least 5 years. chance that more than…
Oxygen demand is a term biologists use to describe the oxygen needed by fish and other aquatic organisms for survival. The Environmental Protection Agency conducted a study of a wetland area. In this wetland environment, the mean oxygen demand was μ = 9.9 mg/L with 95% of the data ranging from 6.3 mg/L to 13.5 mg/L. Let x be a random variable that represents oxygen demand in this wetland environment. Assume x has a probability distribution that is approximately normal. (a) Use the 95% data range to estimate the standard deviation for oxygen demand. (b) An oxygen demand below 8 indicates that some organisms in the wetland environment may be dying. What is the probability that the oxygen demand will fall below 8 mg/L? (Round your answer to four decimal places.) (c) A high oxygen demand can also indicate trouble. An oxygen demand above 12 may indicate an overabundance of organisms that endanger some types of plant life. What is the probability that the oxygen demand will exceed 12…

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