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
