SOLUTION: Please help me with the following question: (It is not in the book, it is on a homework assignment.) The lifetime of a popular dvd player is guaranteed to be 8 years. If the li

Question 108786: Please help me with the following question: (It is not in the book, it is on a homework assignment.)
The lifetime of a popular dvd player is guaranteed to be 8 years. If the lives of this dvd players are normally distributed with a mean of 8.75 and a SD of .45 years, find the percentage of the DVD players that will not meet the guarantee.
Found 2 solutions by Fombitz, edjones:
Answer by Fombitz(13823) (Show Source):
You can put this solution on YOUR website!
Since you've assumed a normal distribution, you can
calculate your z value using the value you're intereted in, the mean and the standard deviation.

where x = 8 years (your warranty date)

Your z score then gives you the percentage of units that failed before 8 years, that is, did not meet the guarantee.
At z=-1.667, the cumulative distribution function (from EXCEL) gives a value of 0.04779.
In other words, from 0 to 8 years, the area under the curve is 4.8% of the total area.
4.8% of the units failed to meet the guarantee.

Answer by edjones(7311) (Show Source):
You can put this solution on YOUR website!
8.75-8.00=.75
.75/.45=1.67 standard deviations from the mean.
We want to know the area under the normal distribution curve only at one end since we are not interested in extreme long life of the DVD players.
The answer in the table is about .05 or 5% will not meet the guarantee.
Ed