It is believed that 4% of children have a gene that may be linked to juvenile di

Question

It is believed that 4% of children have a gene that may be linked to juvenile diabetes. Researchers at a firm would like to test new monitoring equipment for diabetes Hoping to have 22 children with the gene for their study, the researchers test 729 newborns for the presence of the gene linked to diabetes. What is the probability that they find enough subjects for their study? What is the probability? Select the correct answer below and, if necessary, fill in the answer box to complete your choice 0 A. P(enough subjects)- (Round to three decimal places as needed.) O B. The conditions for finding the probability are not satisfied

Explanation / Answer

A. P(enough subjects) = 0.925

Explanation:

p = .04

n = 729

= np = 729*.04 = 29.24

= (np(1-p)) = (729*.04*.96) = 5.3

We will use the normal approximation to the binomial distribution with continuity correction:

P(Y > 22) P(X > 21.5) = P( (x-)/ > (21.5 - 29.16)/5.3 ) = P( z > -1.44) = .925

The probability they have at least 22 children in their study from a sample of 729 is 92.5%

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