Question

8. A company makes electronic components for TV's. 95% pass final inspection (and 5% fail and need to be fixed). 120 components are inspected in one day. (10 points) b.What is the variance of the number that pass inspection in one day

Answer 1

Using the binomial distribution, it is found that the variance of the number that pass inspection in one day is 5.7.

For each component, there are only two possible outcomes, either it passes inspection, or it does not. The probability of a component passing inspections is independent of any other component, hence, the binomial distribution is used to solve this question.

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability, and has variance given by:

$V(X) = np(1 - p)$

In this problem:

• 95% pass final inspection, hence $p = 0.95$

• 120 components are inspected in one day, hence $n = 120$.

The variance is given by:

$V(X) = np(1 - p) = 120(0.95)(0.05) = 5.7$

The variance of the number that pass inspection in one day is 5.7.

To learn more about the binomial distribution, you can take a look at brainly.com/question/24863377