Question

A drug tester claims that a drug cures a rare skin disease 72​% of the time. The claim is checked by testing the drug on 100 patients. If at least 65 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

Claim will be accepted if P[ X >= 65 ]

Claim will be rejected if P[ X < 65 ].

The population proportion of success is p = 0.72, and the sample size is n= 100. We need to compute P[ X < 65 ].

The population mean is computed as:

  

and the population standard deviation is computed as:

Therefore, we get that

so then, we conclude that P[ X < 65 ]. ≈ 0.0739, which ends the calculation of the requested probability