Question

A pharmacist receives a shipment of 1717 bottles of a drug and has 44 of the bottles tested. If 44 of the 1717 bottles are contaminated, what is the probability that no more than 11 of the tested bottles is contaminated? Express your answer as a fraction or a decimal number rounded to four decimal places

Answer 1

0.7633

Explanation:

Proportion of the population that is contaminated = P = (4/17) = 0.235

We now need to find the probability that not more than 1 of the 4 bottles tested is contaminated. This is a binomial distribution problem.

Binomial distribution function is represented by

P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ

n = total number of sample spaces = number of bottles to be tested = 4

x = Number of successes required = 0, 1

p = probability of success = probability that a bottle is contaminated = 0.235

q = probability of failure = probability that a bottle is NOT contaminated = 1 - 0.235 = 0.765

P(X ≤ 1) = P(X=0) + P(X=1) = 0.34248830063 + 0.4208352975 = 0.7633235981 = 0.7633 to 4 d.p

Hope this helps!!!