The U.S. government has devoted considerable funding to missile de-fense research over the past 20 years. The latest development is theSpace-Based Infrared System (SBIRS), which uses saltellite imagery todetect and track missiles (Chance, Summer 2005). The probability ofan intruding object (e.g., a missile) will be detected on a flight trackby SBIRS is 0.8. Consider a sample of 15 simulated tracks, each withan intruding object. Let X equal the number of these tracks on whichSBIRS detects the object.(a) Demonstrate that X is (approximately) a binomial random vari-able(b) Give the value of p and n for the binomial distribution.(c) Find P(X = 8), the probability that SBIRS will detect the objecton exactly 8 tracks.

Answered: The U.S. government has devoted…

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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In a large clinical trial, 399,884 children were randomly assigned to two groups. The treatment group consisted of 201,068 children given a vaccine for a certain disease, and 26 of those children developed the disease. The other 198,816 children were given a placebo, and 91 of those children developed the disease. Consider the vaccine treatment group to be the first sample. Complete parts (a) through (d) below. a. Assume that a 0.10 significance level will be used to test the claim that p₁
The U.S. Energy Information Administration claimed that U.S. residential customers used an average of 10,941 kilowatt hours (kWh) of electricity this year. A local power company believes that residents in their area use more electricity on average than EIA's reported average. To test their claim, the company chooses a random sample of 115 of their customers and calculates that these customers used an average of 11,425 kWh of electricity last year. Assuming that the population standard deviation is 3217 kWh, is there sufficient evidence to support the power company's claim at the 0.02 level of significance? Step 3 of 3: Draw a conclusion and interpret the decision.
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According to the 2000 U.S. Census Bureau, in 2000, 9.5 percent of children in the state of Ohio were not covered by private or government health insurance. In the neighboring state of Pennsylvania, 4.9 percent of children were not covered by health insurance. Assume that these proportions are parameters for the child populations of the respective states. If a random sample of size 100 children is drawn from the Ohio population, and an independent random sample of size 120 is drawn from the Pennsylvania population, what is the probability that the samples would yield a difference, ^p1 - ^p2 of .09 or more?
Each scenario shows the data used for a randomisation test on a difference in two proportions. Both have a sample size of n = 30, with half being assigned to Treatment A and half to Treatment B. Scenario 1 has a difference in proportions of 0.4. Scenario 2 has a difference in proportions of 0.2. If we ran a randomisation test for each scenario, the one that would result in a smaller tail proportion in the resulting re-randomisation distribution is: Scenario 2 Scenario 1 Data Yes Yes Data Yes Yes 01 4 LO 5 02 7 No 03 No 0.2 11 →No 05 11 0.4 06 0.7 10 67 8 No DO 4 09 B B 10
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The United States Bureau of Labor Statistics (BLS) conducts the Quarterly Census of Employment and Wages (QCEW) and reports a variety of information on each county in America. In the third quarter of 2016, the QCEW reported the total taxable earnings, in millions, of all wage earners in all 3222 counties in America. Suppose that James is an economist who collects a simple random sample of the total taxable earnings of workers in 56 American counties during the third quarter of 2016. According to the QCEW, the true population mean and standard deviation of taxable earnings, in millions of dollars, by county are ?=28.29 and ?=33.493 , respectively. Let ? be the total taxable earnings, in millions, of all wage earners in a county. The mean total taxable earnings of all wage earners in a county across all the counties in James' sample is ?⎯⎯⎯ . Use the central limit theorem (CLT) to determine the probability ? that the mean taxable wages in James' sample of 56 counties will be less than…
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6) Any basketball fan knows that Shaquille O’Neal, one of the NBA’s most dominant centers of the last twenty years, always had difficulty shooting free throws. Over the course of his career, his overall made free-throw percentage was 53.3%. During one off-season, Shaq had been working with an assistant coach on his free-throw technique. During the next season, a simple random sample showed that Shaq made 26 of 39 free-throw attempts. Test the claim that Shaq has significantly improved his free-throw shooting using a 0.05 significance level. Check the conditions of the Central Limit Theorem for this scenario. Calculate the number of failures.

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