Question

Replacement times for CD players are normally distributed

with=5.5
years (66 months) and
= 1.5 years (18 months). Find the probabilitythat a randomly
selected CD player will have a replacement time orMORE THAN 7
YEARS.

Answer 1

0.04

Explanation:

X~N(μ=14.2; σ=0.9), a=7

`P(X>7)=1-P(X\leq 7)`

`P(0\leq X\leq a)=P((0-\mu)/(\sigma) \leq (X-\mu)/(\sigma)\leq (a-\mu)/(\sigma)), Z= (X-\mu)/(\sigma)=P(0\leq X\leq a)=P((0-\mu)/(\sigma) \leq (X-\mu)/(\sigma)\leq (a-\mu)/(\sigma)), Z= (X-\mu)/(\sigma)`

`P(0\leq X\leq 7) = P((0-5.5)/(1.5) \leq Z\leq (7-5.5)/(1.5)) = \Phi(1.66)-\Phi(-3.66) = \Phi(1.66) -(1-\Phi(3.66)) = 0.95-(1-0.99)=0.96`

P(X>7)=1-0.96=0.04