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Probability and Statistics for Engineers and the Scientists | 9th Edition | ISBN: 9780321629111 | Authors: Ronald E. Walpole; Raymond H. Myers; Sharon L. Myers; Keying E. Ye
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The Centers for Disease Control and Prevention reported in

Chapter 4, Problem 84E

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QUESTION:

The ?Centers for Disease Control and Prevention reported in 2012 that 1 in 88 American children had been diagnosed with an autism spectrum disorder (ASD). a. If a random sample of 200 American children is selected, what are the expected value and standard deviation of the number who have been diagnosed with ASD? b. Referring back to (a), calculate the approximate probability that at least 2 children in the sample have been diagnosed with ASD? c. If the sample size is 352, what is the approximate probability that fewer than 5 of the selected children have been diagnosed with ASD?

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QUESTION:

The ?Centers for Disease Control and Prevention reported in 2012 that 1 in 88 American children had been diagnosed with an autism spectrum disorder (ASD). a. If a random sample of 200 American children is selected, what are the expected value and standard deviation of the number who have been diagnosed with ASD? b. Referring back to (a), calculate the approximate probability that at least 2 children in the sample have been diagnosed with ASD? c. If the sample size is 352, what is the approximate probability that fewer than 5 of the selected children have been diagnosed with ASD?

ANSWER:

Problem 84E Answer: Step1: We have The Centers for Disease Control and Prevention reported in 2012 that 1 in 88 American children had been diagnosed with an autism spectrum disorder (ASD). 1 That is p = 88 = 0.0114 q = 1 - p = 1 - 0.0114 = 0.9886 We need to find, a. If a random sample of 200 American children is selected, what are the expected value and standard deviation of the number who have been diagnosed with ASD b. Referring back to (a), calculate the approximate probability that at least 2 children in the sample have been diagnosed with ASD c. If the sample size is 352, what is the approximate probability that fewer than 5 of the selected children have been diagnosed with ASD Step2: a). Let X be the number of children, in a random sample of n children that are diagnosed with ASD

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