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

19 children with the gene for their study, the researchers test 732

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.

A.

P(enough

subjects)

(Round to three decimal places as needed.)

B.

The conditions for finding the probability are not satisfied.

Explanation / Answer

Here , X is a random variable which represents number of newborns for the presence of the gene linked to diabetes in a sample of size n=732 & probability of children have a gene that may be linked to juvenile diabetes is p=0.04.

Clearly, X ~ Binomial (n=732,p=0.04)

Proabability mass function of X is ,

P(X=x)=nCxpx(1-p)n-x=732Cx0.04x*0.96732-x ; x=0,1,2,.......,n=732

We have to find here the probability that researchers  find enough subjects for their study i.e. P(X>=19).

Consider,

P(X>=19)=P(X=19)+P(X=20)+P(X=21)+........+P(X=732)

=732C190.0419*0.96732-19 +732C200.0420*0.96732-20+

732C210.0421*0.96732-21+..........+732C7320.04732*0.96732-732

     =0.01088492+ 0.01616864+0.02284141+.........+0

=0.9840198

Hence , answer of this question is option A.

P(enough subjects)=0.984

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