Exercise1. In a manufacturing process where glass productsare made, defects or bubbles occur, occasionallyrendering the piece undesirable for marketing. It isknown that, on average, 1 in every 1000 of theseitems produced has one or more bubbles. What isthe probability that a random sample of 8000 willyield fewer than 7 items possessing bubbles?Let n=8000p=0.001

The binomial distribution is a discrete probability distribution in which there are a fixed number…

Answered: Exercise 1. In a manufacturing process…

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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A sample of n=64 observation (independently drawn) is selected from a population with mean 20 and s.d.16. What is the probability that the sample mean is less than 15.5?
2. The number of patients visiting an emergency room during the graveyard shift (11:00pm-7:00pm), denoted by the random variable X, has the following probability distribution: 1 2 3 4 5 P(X=x) .05 .20 .25 .20 .10 .15 .05 a. Find the probability there will be 3 or more emergency room patients during a randomly selected 8-hour graveyard shift. b. Find the probability there will be an even number of patients. c. Find the probability there will be at least 2 but not more than 5 patients. d. Find the probability there will be less than 2 patients. e. How do you suppose the probability distribution above was obtained?
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Recall that Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Now suppose you are the auditor for a very large corporation. The revenue file contains millions of numbers in a large computer data bank. You draw a random sample of n = 226 numbers from this file and r = 87 have a first nonzero digit of 1. Let p represent the population proportion of all numbers in the computer file that have a leading digit of 1. 1) Test the claim that p is more than 0.301. Use α = 0.10. 2) What is the value of the sample test statistic? (Round your answer to two decimal places.) 3) Find the P-value of the test statistic. (Round your answer to four decimal places.) 4) If p is in fact larger than 0.301, it would seem there are too many numbers in…
A pharmaceutical company receives large shipments of ibuprofen tablets and uses an acceptance sampling plan. This plan randomly selects and tests 26 tablets, then accepts the whole batch if there is at most one that doesn't meet the required specifications. What is the probability that this whole shipment will be accepted if a particular shipment of thousands of ibuprofen tablets actually has a 12% rate of defects? (Report answer as a decimal value accurate to four decimal places.) P(accept shipment) =
A news article estimated that only 6% of those ages 65 and older who prefer to watch the news, rather than to read or listen, watch the news online. This estimate was based on a survey of a large sample of adult Americans. Consider the population consisting of all adult Americans ages 65 and older who prefer to watch the news, and suppose that for this population the actual proportion who prefer to watch online is 0.06. (a) A random sample of n = 100 people will be selected from this population and p̂, the proportion of people who prefer to watch online, will be calculated. What are the mean and standard deviation of the sampling distribution of p̂? (Round your standard deviation to four decimal places.) meanstandard deviation (b) Is the sampling distribution of p̂ approximately normal for random samples of size n = 100? Explain. (Select all that apply.) the sampling distribution of p̂ is approximately normalthe sampling distribution of p̂ is not approximately normalnp is…
1. A university has 25,000 students, of whom 17,000 are undergraduates. The housing office takes a simple random sample of 500 students; 357 out of the 500 are undergraduates. Fill in the blanks. (If necessary, round using 2 decimal places. For percentages, enter a number between 0 and 1) (a) For the number of undergraduates in the sample, the observed value is _________ but the expected value is ______________ (b) For the percentage of undergraduates in the sample, the observed value is ____________ but the expected value is ____________
Among 10 laptop computers, 8 are good and 2 have defects. Unware of this, a customer buys 3 laptops. (a) What is the probability of exactly 2 defective laptops among them? (b) What is the probability of at least 1 defective laptops among them

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