Answer:
Step-by-step explanation:
Binomial distribution is to be used here due to following reasons.
(a)
Probability of sending a box to an experienced inspector
= Probability of getting non-zero unacceptable cans
= 1 - Probability of getting zero unacceptable cans
=1- P(X = 0) = 1 - 10.08^0 *(1 – 0.08)^(4-0) = 0.283607
(b)
Expected cost per inspector in an hour in case of 8% unacceptable cans
= {(1-0.283607)*16+0.283607*22} = $ 17.70164
If groceries reduce their unacceptable rate to 4% then X - Bin(4, 0.04) .
In this scenario,
Probability of sending a box to an experienced inspector
= Probability of getting non-zero unacceptable cans
= 1 - Probability of getting zero unacceptable cans
=1- P(X = 0) = 1 - 0.04^0 * (1 – 0.04)*(4-0) = 0.150653
Expected cost per inspector in an hour in case of 4% unacceptable cans
= {(1-0.150653)*16+0.150653*22} = $ 16.90392
Percentage of savings realized = (17.70164-16.90392)/17.70164*100% = 4.506475%
