MATH SOLVE

3 months ago

Q:
# A particular sale involves four items randomly selected fromalarge lot that is known to contain 10% defectives. Let Y denotethenumber of defectives among the four sold. The purchaser oftheitems will return the defectives for repair, and the repair costisgiven by C = 3Y^2 + Y + 2. Find the expected repair cost.

Accepted Solution

A:

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 = 0.10Let 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.