Question

Bob is doing a quality test on machine bolts. He tested 24 bolts that he randomly picked and found that 5 were defective Based on Bob's results, what is the expected number of bolts that will be defective if he tests 840 bolts?​

Answer 1

Mean of the binomial distribution

μ = 174.972 bolts

Explanation:

Step(i):-

Given that Bob tested 24 bolts that he randomly picked and found that 5 were defective

The proportion of the defective item

`p = (x)/(n) = (5)/(24) = 0.2083`

Step(ii):-

Let 'x' be a random variable in a binomial distribution

Mean of the binomial distribution

μ = np

μ = 840 ×0.280

μ = 174.972

Final answer:-

Mean of the binomial distribution μ = 174.972 bolts