SOLUTION: 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 playe

Question 1087324: 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.

Answer by mathmate(429) (Show Source): You can put this solution on YOUR website!
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-μ)/σ)
=P(z<(2-2.5)/0.4)
=P(z<-1.25)
=0.1056 [ from normal probability tables ]

3. P(z From tables, Z=-0.67449 has an area of 25% on the left tail =>
[This translates to x=(σZ)+μ=2.23 years]

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