In a study of 307,992 cell phone users, it was found that 85 developed cancer of
ID: 3155555 • Letter: I
Question
In a study of 307,992 cell phone users, it was found that 85 developed cancer of the brain or nervous system. Assuming that cell phones have no effect, there is a 0.000285 probability of a person developing cancer of the brain or nervous system. We therefore expect about 88 cases of such cancer in a group of 307,992 people. Estimate the probability of 85 or fewer cases of such cancer in a group of 307,992 people. What do these results suggest about media reports that cell phones cause cancer of the brain or nervous system?
P(x85)=_________(round to 4 decimal places as needed)
Explanation / Answer
Here,
n = 307992
p = 0.000285
We first get the z score for the critical value:
x = critical value = 85.5
u = mean = np = 87.77772
s = standard deviation = sqrt(np(1-p)) = 9.367641291
Thus, the corresponding z score is
z = (x-u)/s = -0.243147654
Thus, the left tailed area is
P(z < -0.243147654 ) = 0.403945508 [ANSWER]
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Hi! I used normal approximation to the binomial here. If you use another method of approximation here, please resubmit this question together with the method you prefer in calculating the probability. That way we can continue helping you! Thanks!