Question

Large lots of spark plugs are being inspected for quality. A lot is considered acceptable if 5% or fewer of the spark plugs are defective. A random sample of 5 spark plugs is selected from a given lot. If the lot is unacceptable, with 40% defective spark plugs, what is the probability that exactly 3 of the spark plugs in the sample are defective?

Answer 1

Solution

Given that ,

p = 0.40

1 - p = 1 - 0.40 = 0.60

n = 5

Using binomial probability formula ,

P(X = x) = (_n C _x) * p^x * (1 - p)^{n - x}

P(X = 3) = (₅ C ₃) * (0.40)³ * (0.60)²

Probability = 0.2304