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 4 or more parts out of a sample of 60 to be defective?
A) 4.85%
B) 0.49%
C) 15.62%
D) Almost 50%
E) 22.96%

Question

Quizplus · Accepted Answer

This is a binomial probability problem with n=60, p=0.02, and we want to find the probability of getting 4 or more defective parts. This can be solved using the binomial cumulative distribution function or a normal approximation to the binomial distribution. 
Using binomial distribution function, we get P(X ≥ 4) = 1 - P(X ≤ 3) = 1 - binom.cdf(3, 60, 0.02) ≈ 0.0049 or 0.49% (using a calculator or software). 
Using a normal approximation to the binomial (with mean μ = np = 1.2 and standard deviation σ = sqrt(np(1-p)) = 1.0897), we can standardize the distribution as Z = (X - μ)/σ and use the standard normal distribution table to find P(Z ≥ (4-μ)/σ) = P(Z ≥ 2.71) ≈ 0.003. This is close to the exact binomial probability and gives similar results. 
Therefore, the best choice is B: 0.49%.

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