Respuesta :
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[tex]C = 3Y^2 + Y + 2[/tex]
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
[tex]E(Y)=np = 4 \times 0.10 =0.4[/tex]
[tex]V(Y)=np(1-p)=0.4(1-0.1)=0.36[/tex]
Now we know that [tex]V(Y)=E(Y^2)-[E(Y)]^2[/tex]
[tex]0.36=E(Y^2)-[0.4]^2[/tex]
[tex]0.36=E(Y^2)-0.16[/tex]
[tex]0.36+0.16=E(Y^2)[/tex]
[tex]0.52=E(Y^2)[/tex]
Now we are given an equation that represents the repair cost
[tex]C = 3Y^2 + Y + 2[/tex]
So, Expected repair cost = [tex]E(C) =E( 3Y^2 + Y + 2)[/tex]
[tex]E(C) =3E(Y^2) +E(Y) + 2[/tex]
[tex]E(C) =3 \times 0.52 +0.4+ 2[/tex]
[tex]E(C) =3.96[/tex]
Hence the expected repair cost is 3.96.
