A pharmaceutical company has produced an experimental medici

A pharmaceutical company has produced an experimental medicine to control cancer cells from replication with a success rate of 90%. The medicine is administered to 20 cancer patients in a clinical trial (The trail for the 20 patients is independent.) Let X be the number of patents whose cancer cells stopped replication. What type of probability distribution is the rate of success would follow? Explain why? What is the probability that the medicine will cure all of the 20 patients ? What is the probability probability that half patients cured?

Solution

a. Rate of success = X/20 will follow a Binomial distribution with mean p = 0.90 and variance = p(1-p)/n = 0.9*0.1/20

This is because the 20 trials are independent of each other and the rate of success is same (0.90) for each trial.

b. P(X=20) = 20C20*(0.90)²⁰ *(1-0.90)^20-20 = 0.1216

P(X=10) = 20C10*(0.90)¹⁰ *(1-0.90)^20-10 = 0.000006442