Question

A machine produces an average of 10% defective bolts. A batch is accepted if a sample of 5 bolts take from that batch contains no defective, and rejected if the sample contains 3 or more defectives. In other cases, a second sample is taken.

a) What is the probability that the second sample will be required?

b) What is the probability that the sample is rejected?

c) If 15 bolts are taken from a batch, how many bolts are expected to be defective?

Pls show work so I can learn step by step

Answer 1

Let X is a random variable shows the number of defective bolts out of 5. Here X has binomial distribution with parameters as follow:

n=5 and p=0.10

(a)

The probability that the second sample will be required, that is at least one defective and at most 2 defectives, is

(b)

The probability that the sample is rejected is

(c)

The number of expected defective bolts is