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?

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

Step-by-step 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