Question

It is believed that 44​% 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 735 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. (Please show how to calculate on TI-84 Plus)

A.P(enough subjects)equals = ???

​(Round to three decimal places as​ needed.)

B.The conditions for finding the probability are not satisfied.

Answer 1

n=

735

p=

0.0400

here mean of distribution=μ=np=	29.40
and standard deviation σ=sqrt(np(1-p))=	5.31
for normal distribution z score =(X-μ)/σx

therefore from normal approximation of binomial distribution and continuity correction:

A.P(enough subjects):

probability =P(X>21.5)=P(Z>(21.5-29.4)/5.313)=P(Z>-1.49)=1-P(Z<-1.49) =1-0.0681=0.932

(Note

if using ti-84 press 2nd -vars- use command :normalcdf(21.5,1000000,29.4,5.3126)