Question

Suppose that a pharmaceutical company claims that it has a new cure for the flu, and that %96 of flu sufferers will fully recover within 24 hours of taking the drug. As a first test on the claim, a clinic will give the drug to 25 people diagnosed with the flu and check on their condition 24 hours later. Suppose that company’s claim is perfectly accurate.
1. Let random variable X be the number of people tested who will recover from the flu in 24 hours. What can we say about the probability distribution of X?
2. What is the chance that all 25 people tested will recover within 24 hours?
3. What is the chance that the percentage tested who recover will exactly match the claimed percentage?
4. What is the probability that only %80? of the people tested recover within 24 hours?

Answer 1

1. X be the number of people tested who will recover from the flu in 24 hours.

Probability distribution of X would be BINOMIAL.

X ~ BINOMIAL (n = 25, p = 0.96)

(2) P(All 25 people will recovr withing 24 hours) = 0.9625 = 0.3604

(3) P(X = 24) = 25C24 (0.96)24 (0.04) = 0.3754

(3) 80% of the people tested recover = 80% * 25 = 20

P(x = 20) = 25C20 (0.96)20 (0.04)5 = 0.0024