Question

A drug tester claims that a drug cures a rare skin disease 68​% of the time. The claim is checked by testing the drug on 100 patients. If at least 60 patients are​ cured, the claim will be accepted.

Find the probability that the claim will be rejected assuming that the​ manufacturer's claim is true. Use the normal distribution to approximate the binomial distribution if possible.

Answer 1

P(curing the disease), p = 0.68

q = 1 - p = 0.32

Sample size. n = 100

np = 100x0.68 = 68

np = 100x0.32 = 32np and nq 5. So, normal approximation to binomial distribution can be used.

P(X < A) = P(Z < (A - mean)/standard deviation)

Mean = 100 x 0.68 = 68

Standard deviation =

=

= 4.665

P(at least 60 patients are​ cured) = P(X 60)

= 1 - P(X < 59.5) (continuity correction applied)

= 1 - P(Z < (59.5 - 68)/4.665)

= 1 - P(Z < -1.82)

= 1 - 0.0344

= 0.9656