Question

A quality-control plan calls for accepting a large lot of crankshaft bearings if a sample of seven is drawn and none are defective. What is the probability of accepting the lot if none in the lot are defective?

Answer 1

The probability of accepting the lot if none in the lot are defective is 1.

Explanation:

A large lot of crankshaft bearings is accepted if 0 out of 7 are found defective. i.e. the probability of finding a defective crankshaft is 0.

Let X be the number of defective crankshafts. We need to find the probability that X=0. We will use the binomial distribution probability formula:

P(X=x) = ⁿCₓ pˣ qⁿ⁻ˣ

where n = total no. of trials

x = no. of successful trials

p = probability of success

q = probability of failure (1-p)

We have n=7, p=0, q=1.

P(X=0) = ⁷C₀ (0)⁰ (1)⁷⁻⁰

P(X=0) = 1