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A set of 200 independent patients take antiacid medication

Applied Statistics and Probability for Engineers | 6th Edition | ISBN: 9781118539712 | Authors: Douglas C. Montgomery, George C. Runger ISBN: 9781118539712 55

Solution for problem 108E Chapter 4.7

Applied Statistics and Probability for Engineers | 6th Edition

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Applied Statistics and Probability for Engineers | 6th Edition | ISBN: 9781118539712 | Authors: Douglas C. Montgomery, George C. Runger

Applied Statistics and Probability for Engineers | 6th Edition

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Problem 108E

A set of 200 independent patients take antiacid medication at the start of symptoms, and 80 experience moderate to substantial relief within 90 minutes. Historically, 30% of patients experience relief within 90 minutes with no medication. If the medication has no effect, approximate the probability that 80 or more patients experience relief of symptoms. What can you conclude about the effectiveness of this medication?

Step-by-Step Solution:

Step 1 of 2:  

     Given  n = 200,

     P = the probability of success in each trial

       

    Let X = binomial random variable of patients experiencing relief from symptoms.

   Normal approximation is good for np > 5, and n(1-p) >5.

  Then,

             np = 200(0.4) = 80 > 5 and

            n(1-p) = 200(1-0.4) = 120 > 5.

       Z = standard normal random variable

              

 

 

Step 2 of 2

Chapter 4.7, Problem 108E is Solved
Textbook: Applied Statistics and Probability for Engineers
Edition: 6
Author: Douglas C. Montgomery, George C. Runger
ISBN: 9781118539712

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