Question

A pharmaceutical company claims that a drug cures a rare skin disease 75% of the time. The claim is checked by testing the drug on 200 patients. If at least 140 patients are cured, then this claim will be accepted. Use this information to answer the following two questions. 1)Find the probability that the claim will be rejected, assuming that the manufacturer's claim is true. 2.) Find the probability that the claim will be accepted, assuming that the actual probability that the drug cures the skin disease is 65%.​

Answer 1

probability that the claim will be accepted, assuming the actual probability of cure is 65%, is approximately 0.9631 or 96.31%.

Explanation:

Apologies for the confusion earlier. Let's calculate the probabilities based on the given information:

1) Find the probability that the claim will be rejected, assuming that the manufacturer's claim is true:

Using the normal approximation, we can find the z-score corresponding to X = 139. We standardize the random variable as follows:

Z = (X - μ) / σ

Z = (139 - 150) / sqrt(37.5) ≈ -1.795

Now we can find the probability using the standard normal table or a calculator:

P(Z < -1.795) ≈ 0.0369

Therefore, the probability that the claim will be rejected, assuming the manufacturer's claim is true, is approximately 0.0369 or 3.69%.

2) Find the probability that the claim will be accepted, assuming that the actual probability that the drug cures the skin disease is 65%:

Using the normal approximation, we can find the z-score corresponding to X = 139:

Z = (139 - 150) / sqrt(37.5) ≈ -1.795

Now we can find the probability:

P(Z > -1.795) ≈ 1 - P(Z < -1.795) ≈ 1 - 0.0369 ≈ 0.9631

Therefore, the probability that the claim will be accepted, assuming the actual probability of cure is 65%, is approximately 0.9631 or 96.31%.

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