Question

A particular sale involves four items randomly selected from

alarge lot that is known to contain 10% defectives. Let Y denote
thenumber of defectives among the four sold. The purchaser of
theitems will return the defectives for repair, and the repair cost
isgiven by C = 3Y^2 + Y + 2. Find the expected repair cost.

Answer 1

The expected repair cost is 3.96.

Explanation:

Given :A particular sale involves four items randomly selected from a large lot that is known to contain 10% defectives.

The purchaser of the items will return the defectives for repair, and the repair cost is given by
`C = 3Y^2 + Y + 2`

To Find : Find the expected repair cost.

Solution:

We are given that A particular sale involves four items randomly selected from a large lot that is known to contain 10% defectives.

So, The probability of item being defected = 0.10

Let Y denote the number of defectives among the four sold.

It follows the binomial distribution.

n = 4 , p =0.10

`E(Y)=np = 4 * 0.10 =0.4`

`V(Y)=np(1-p)=0.4(1-0.1)=0.36`

Now we know that
`V(Y)=E(Y^2)-[E(Y)]^2`

`0.36=E(Y^2)-[0.4]^2`

`0.36=E(Y^2)-0.16`

`0.36+0.16=E(Y^2)`

`0.52=E(Y^2)`

Now we are given an equation that represents the repair cost

`C = 3Y^2 + Y + 2`

So, Expected repair cost =
`E(C) =E( 3Y^2 + Y + 2)`

`E(C) =3E(Y^2) +E(Y) + 2`

`E(C) =3 * 0.52 +0.4+ 2`

`E(C) =3.96`

Hence the expected repair cost is 3.96.