Question

12. A quality control procedure at a manufacturing facility involves selecting 5 items at random from a large batch, and then accepting the entire batch if at least 3 of the selected items pass inspection. If in reality 80% of all items produced would individually pass inspection, what is the probability that the batch will be accepted

Answer 1

Answer:

The probability is 0.9421

Step-by-step explanation:

Here, we want to calculate the probability that the batch will be accepted

For it to be accepted, 3,4 or 5 of the items would pass inspection

let p be the probability of a single item

passing the inspection

This probability is 80% = 0.8

Let q be the probability of failing inspection = 2-0.8 = 0.2

The Bernoulli approximation of the probability distribution for 3 passing the inspection out of five will be;

5 C 3 0.8^3 0.2^2 = 0.2048

Next we calculate for 4 out of the five

That will be

5 C 4 0.8^4 0.2 = 0.4096

Finally we calculate for all 5

5 C 5 0.8^5 0.2^0 = 0.32768

So the probability that the batch will be accepted will be;

0.32768 + 0.4096 + 0.2048 = 0.94208