In a study of 385, 664 cell phone users, it was found that 129 developed cancer

Question

In a study of 385, 664 cell phone users, it was found that 129 developed cancer of the brain or nervous system. Assuming that cell phones have no effect, there is a 0 000341 probability of a person developing cancer of the brain or nervous system. We therefore expect about 132 cases of such cancel in a group of 385, 664 people. Estimate the probability of 129 or fewer cases of such cancer in a group of 385, 664 people. What do these results suggest about media reports that cell phones cause cancer of the brain or nervous system? (a) P (x lessthanorequalto 129) = (Round to four decimal places as needed.)

Explanation / Answer

required answer is 0.4137

let x=person develop cancer

here n=385664 and p=0.000341

using binomial distribution property

E(x)=np=385664*0.000341=131.51

sd(x)=sqrt(np(1-p)=sqrt(385664*0.000341*(1-0.000341))=11.47

now we use standard normal variate z=(x-E(x))/sd(x)

for x=129, z=(129-131.5)/11.47=-0.218

P(x<=129)=P(z<-0.218)=0.4137

required answer is 0.4137

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