Stats: Modeling the World Nasta Edition Grades 9-12
Stats: Modeling the World Nasta Edition Grades 9-12
3rd Edition
ISBN: 9780131359581
Author: David E. Bock, Paul F. Velleman, Richard D. De Veaux
Publisher: PEARSON
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Chapter 18, Problem 24E
To determine

To find out what is the probability that they find enough subjects for their study.

Expert Solution & Answer
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Answer to Problem 24E

  0.09608 .

Explanation of Solution

It is given in the question that 4% of children have a gene that may be linked to juvenile diabetes. And the researchers hoping to track 20 of these children for several years test 732 new-borns for the presence of this gene. Thus, let us first verify the assumptions and conditions for the analysis as:

Random condition: It is satisfied as we assume that the children were randomly selected.

  10% condition: The sample size less than 10% of the population size.

Success/failure condition: as np=29.28,n(1p)=702.72 and both are greater than ten then this is also true.

Thus, all the conditions and assumptions are met. Thus, now find the mean and the standard deviation for the following as:

  μ=p=0.04σ=pqn=0.04(0.96)732=0.072

Thus, let us find the z -score to standardized as:

  z=207320.040.072=1.761

So, the probability that the shipment will be accepted anyway is calculated as:

  P(z<1.761)=normalcdf(E99,1.761,0,1)=0.09608

Therefore, the probability that they find enough subjects for their study is 0.09608 .

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