Question

In a study of 432,229 cell phone​ users, it was found that 89 developed cancer of the brain or nervous system. Assuming that cell phones have no​ effect, there is a 0.000213 probability of a person developing cancer of the brain or nervous system. We therefore expect about 93 cases of such cancer in a group of 432,229 people. Estimate the probability of 89 or fewer cases of such cancer in a group of 432,229 people. What do these results suggest about media reports that cell phones cause cancer of the brain or nervous​ system?

(a) P(x≤89)equals=

Answer 1

(a) This is a binomial distribution, but the numbers are large enough that we can use the normal distribution to approximate it.

For a binomial, the mean u = np and the standard deviation is s = √[np(1-p)]. Here, they tell us that u = 93. s = √[(432229)(0.000213)(1 - 0.000213) = 9.59

Now that we have u and s, we can use our normal distribution tables to find P(X < 89). Before we do though, we change 89 to 89.5 to ensure cases where X = 89 are included. Since the binomial distribution is discrete and can't take decimal values, this won't cause any unwanted results to be included.

So P(X < 89.5) = P(Z < (89.5 - 93)/9.59) = P(Z <-0.36 ) = 0.3594