Question

A particular sale involves four items randomly selected from

Answer 1

Answer:

The expected repair cost is 3.96.

Step-by-step 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

$E(Y)=np = 4 \times 0.10 =0.4$

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

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

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

$E(C) =3 \times 0.52 +0.4+ 2$

$E(C) =3.96$

Hence the expected repair cost is 3.96.