SOLUTION: The lifetime of a color television is normally distributed with a mean of 7.8 years and a standard deviation of 3 years. What is the probability that a TV will last more than 10 ye

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Question 353660: The lifetime of a color television is normally distributed with a mean of 7.8 years and a standard deviation of 3 years. What is the probability that a TV will last more than 10 years? more than 7.8 years? How long should the warranty period be (in years) if they want to replace only 1% of the TVs?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Find the z-score.
z=%28x-mu%29%2Fsigma
z=%2810-7.8%29%2F3=0.7333
P%28z%29=0.841345
So then
P%28x%3E10%29=1-0.841345=0.158655
.
.
.
z=%287.8-7.8%29%2F3=0
P%28z%3E7.8%29=0.5
.
.
.
P%28z1%29=0.01
z1=-2.57583
x1=-2.57583%283%29%2B7.8
x1=0.072512 years