Question

Integrated circuits from a certain factory pass a particular quality test with probability 0.75. The outcomes of all tests are mutually independent. (a) What is the expected number of tests necessary to find 680 acceptable circuits?

Answer 1

The expected number of tests necessary to find 680 acceptable circuits is 907.

Explanation:

For each circuit, there are only two possible outcomes. Either it passes the test, or it does not. The probability of a circuit passing the quality test is independent of other circuits. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

The expected number of trials for r successes, with p probability, is given by:

`E = (r)/(p)`

Integrated circuits from a certain factory pass a particular quality test with probability 0.75.

This means that
`p = 0.75`

a) What is the expected number of tests necessary to find 680 acceptable circuits?

This is E when r = 680.

`E = (r)/(p)`

`E = (680)/(0.75)`

`E = 907`

The expected number of tests necessary to find 680 acceptable circuits is 907.