## The probability that a machine part is defective is 0.1. Find the probability that no more than 2 out of 12 parts tested are defective.

Question

The probability that a machine part is defective is 0.1. Find the probability that no more than 2 out of 12 parts tested are defective.

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2 months 2021-10-06T19:18:14+00:00 1 Answer 0 views 0

Probability that no more than 2 out of 12 parts tested are defective is 0.8891.

Step-by-step explanation:

We are given that the probability that a machine part is defective is 0.1.

Twelve parts are selected at random.

The above situation can be represented through binomial distribution; where, n = number trials (samples) taken = 12 parts

r = number of success = no more than 2

p = probability of success which in our question is probability that

a machine part is defective, i.e; p = 0.1

Let X = Number of machine parts that are defective

So, X ~ Binom(n = 12, p = 0.1)

Now, Probability that no more than 2 out of 12 parts tested are defective is given by = P(X 2)

P(X 2) =  P(X = 0) + P(X = 1) + P(X = 2)

= = =  0.8891

Therefore, probability that no more than 2 out of 12 parts tested are defective is 0.8891.