Question

In a study of 389,845 cell phone​ users, it was found that 172 developed cancer of the brain or nervous system. Assuming that cell phones have no​ effect, there is a 0.0004630 probability of a person developing cancer of the brain or nervous system. We therefore expect about 181 cases of such cancer in a group of 389,845 people. Estimate the probability of 172 or fewer cases of such cancer in a group of 389 comma 389,845 people. What do these results suggest about media reports that cell phones cause cancer of the brain or nervous​ system?

Answer 1

Let X is a random variable shows the number of cases of cancer out of 389845 people. Here X has binomial distribution with parameters n=389845 and p=0.0004630.

Since no and n(1-p) both are greater than 5 so we can use normal approximation here. That is X has normal distribution with mean

and standard deviation

The z-score for X =172+0.5 = 172.5 is

So required probability is