A multinational business unit has an examination system for the batches of venti

foass77W

foass77W

Answered question

2021-09-25

A multinational business unit has an examination system for the batches of ventilator units bought from dealers. A batch typically comprises 40 ventilators. In the inspection system, a random sample of 20 is selected and all are tested. Suppose there are 5 faulty ventilators in the batch of 40. What is the probability that for a given sample there will be 2 faulty ventilator?"

Answer & Explanation

Nola Robson

Nola Robson

Skilled2021-09-26Added 94 answers

Step 1
The binomial probability distribution is,
P(X=x)=(nx)(p)x(1p)nx
In the distribution, n denotes the number of trails, p denotes probability of success, and x denotes the number of success.
The random variable X is defined as the number of faulty ventilators which follows binomial distribution with sample size 20 and probability of success 0.125(=540)
Step 2
The probability that there would be 2 faulty ventilator is,
P(X=2)=(202)(0.125)2(10.125)202
=190×0.015625×0.090395
=0.2684
Thus, the probability that there would be 2 faulty ventilator is 0.2684.

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