Question

In a study of 259 comma 995 cell phone​ users, it was found that 121 developed cancer of the brain or nervous system. Assuming that cell phones have no​ effect, there is a 0.000486 probability of a person developing cancer of the brain or nervous system. We therefore expect about 127 cases of such cancer in a group of 259 comma 995 people. Estimate the probability of 121 or fewer cases of such cancer in a group of 259 comma 995 people. What do these results suggest about media reports that cell phones cause cancer of the brain or nervous​ system?

Answer 1

The probability of having 121 cases or less is:

`P(X<121)=P(z<-0.5338)=0.2967`

This suggests that the study does not show any significantly effect of the use of cell phone in the probability of having brain or nervous system cancer. The use of cell phone does not appear to be a significant factor in the risk of having this type of cancer.

Explanation:

We start by calculating the expected standard deviation of the population cases:

`\sigma=√(n\pi(1-\pi))=√(259,995*0.000489*0.999514)\\\\\sigma=√(126.29)\\\\\sigma=11.24`

Then, to calculate the probability, we first calculate the z-score for 121 cases.

`z=(X-\mu)/(\sigma)=(121-127)/(11.24)=(-6)/(11.24)=-0.5338`

The probability of having 121 cases or less is:

`P(X<121)=P(z<-0.5338)=0.2967`

This suggests that the study does not show any significantly effect of the use of cell phone in the probability of having brain or nervous system cancer. The use of cell phone does not appear to be a significant factor in the risk of having this type of cancer.