Dawson's Repair Service orders parts from an electronic company who advertises its parts o be no more than 2% defective. What is the probability that Bill Dawson finds 3 or more parts out of a sample of 50 to be defective?
A) Almost 100%
B) 0.0217
C) 15.62%
D) Almost 50%
E) 34.38%

Question

Quizplus · Accepted Answer

This is a binomial distribution problem with n=50 and p=0.02 (probability of defective parts). The formula for finding the probability of at least 3 defective parts is:

P(X≥3) = 1 - P(X<3) = 1 - [P(X=0) + P(X=1) + P(X=2)]

Using the binomial formula, we can find each of these probabilities:

P(X=0) = (50 choose 0) * 0.02^0 * 0.98^50 = 0.364
P(X=1) = (50 choose 1) * 0.02^1 * 0.98^49 = 0.377
P(X=2) = (50 choose 2) * 0.02^2 * 0.98^48 = 0.186

So, P(X≥3) = 1 - (0.364 + 0.377 + 0.186) = 0.073 or 7.3%.

Therefore, the best choice is B) 0.0217 (rounded to four significant figures).

Dawson's Repair Service Orders Parts from an Electronic Company Who