In a study of 202, 525 cell phone users, it was found that 53 developed cancer o

Question

In a study of 202, 525 cell phone users, it was found that 53 developed cancer of the brain or nervous system. Assuming that cell phones have no effect, there is a 0.000289 probability of person developing cancer of the brain or nervous system. We therefore expect about 59 cases of such cancer in a group of 202, 525 people. Estimate the probability of 53 or fewer cases of such cancer in a group of 202, 525 people. What do these results suggest about media reports that cell phones cause cancer of the brain or nervous system? (a) P(x lessthanorequalto 53) = (Round to four decimal places as needed.)

Explanation / Answer

n = 202525

p = 0.000289

P(X <= 53)

X is binomial (n,p)

we can approximate using normal distribution

mean = np = 58.529725

sd = sqrt(npq) = 7.649366635

Z= (X - 58.529725)/7.649366635

P(X<= 53)

P(X < 53.5) continuity correction

P(Z< (53.5 - 58.529725)/7.649366635)

P(Z<   -0.657534)

=0.255399

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