Answer:
n=410 (sample of headache sufferers)
p = 0.637 (proportion of those who get relief with just two aspirins)
Mean = np = (410)(0.637) = 261.17
Standard deviation = sqrt [ np(1-p)] = sqrt [ (410)(0.637)(0.363)] = 9.7368
We want the probability that more than 66.2% obtain relief.
(410)(0.662) = 271.42
Using the normal distribution with mean 261.17 and standard deviation 9.7368:
ÎĽ = 261.17
Ď = 9.7368
standardize x to z = (x - ÎĽ) / Ď
P(x > 271.42) = P( z > (271.42-261.17) / 9.7368)
= P(z > 1.0527) = 0.1469
(probability that in a random sample of 410 headache sufferers, more than 66.2% obtain relief)
