A certain antibiotic in known to cure 85% of strep bacteria infections.

Question

    A scientist wants to make sure the drug does not lose its potency over time. He treats 100 patients with a 1 year old supply of the antibiotic. Let  p* be the proportion of individuals who are cured. What is the sampling distribution of p*?What is the probability that more than 90% in the sample are cured?

Answer 1

The sampling distribution of p*: mean equals population value (p) = 0.85, standard deviation = (p(1-p)/n)^0.5 = ((0.85*0.15/100)^0.5 = 0.357

Will use standardized normal table to determine probability.

P(p* > 0.9) = P(z > (0.9 - 0.85) / 0.357) = P(z > 0.14) = P (z < -0.14) = 0.4946