A drug tester claims that a drug cures a rare skin disease 8

A drug tester claims that a drug cures a rare skin disease 82% of the time. The claim is checked by testing the drug on 100 patients. If at least 76 patients are cured, the claim will be accepted. Find the probability that the claim will be rejected assuming that the manufacterer\'s claim is true. Use the normal distribution to approximate the binomial distribution, if possible.

Solution

N = 100
P = 0.82
Q = 0.18

Mean = np = 82
Sd = sqrt(npq) = sqrt(14.76) = 3.84

So, the probability that the claim will be rejected assuming that the manufacturer\'s claim is true is

P(Z > (X-Mean)/sd)

= P(Z > (76 - 82)/ 3.84)

= P(Z > -1.56)

= 0.6950