Question 1087324
Question:
1.  Sunshine Stereo sells cd players. The cd players life is normally distributed with a mean of 2.5 years and a standard deviation of 0.4 years. What is the z score for a cd player will break down during the guarantee period of 2 years? 
2.Using Table 3, find the probability
3.Find the z score so that 25% of the standard normal curve lies to the left of z. 
 
Solution:
μ=2.5 years
σ=0.4 years
 
1. z-score = (x-μ)/σ=(2-2.5)/0.4=-1.25
 
2. P(x<2)
P(x<2)
=P(z<(2-&mu;)/&sigma;)
=P(z<(2-2.5)/0.4)
=P(z<-1.25)
=0.1056  [ from normal probability tables ]
 
3. P(z<Z)=0.25
From tables, Z=-0.67449  has an area of 25% on the left tail =>
[This translates to x=(&sigma;Z)+&mu;=2.23 years]