Question

A company makes electric motors. The probability an electric motor is defective is 5% . What is the probability that a sample of 100 electric motors will contain no defective motor? Use just one decimal point!

Answer 1

Explanation:

The probability an electric motor is defective is 5%. This means that the probability of success, p = 5/100 = 0.05

The probability of failure, q = 1 - p = 1 - 0.05 = 0.95.

number of samples is 100, so n = 100

We would apply binomial distribution. The formula for binomial distribution is expressed as

P(x = r) = nCr × q^(n - r) × p^r

We want to determine the probability that there would be no defective. This is expressed as

P(x = 0) = 100C0 × 0.95^(100- 0) × 0.05^0 = 1 × 0.0059 × 1 = 0.006