SOLUTION: Life time of an automatic dishwasher is normally distributed with mean 3.5 years and S.D = 1.0 yrs. If a dishwasher is guaranteed for 12 months, what is the fraction of the sale

Question 1073724: Life time of an automatic dishwasher is normally distributed with mean 3.5 years
and
S.D = 1.0 yrs. If a dishwasher is guaranteed for 12 months, what is the fraction of the sale that will require replacement? Mean 2,5 and SD 1.5 yrs guaranteed 6 months.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
calculator used can be found at this link:

http://davidmlane.com/hyperstat/z_table.html

mean = 3.5 years = 42 months
standard deviation = 1 year - 12 months
guaranteed for 12 months.
approximately .62% of the machines will fail within the first 12 months.

$$$

mean = 2 years = 24 months
standard deviation = 1.5 years = 18 months
guaranteed for 6 months.
approximately 15.87% of the machines will fail within the first 6 months.

$$$

this calculator allows you to use raw scores or z-scores.

z-score = (x-m)/s

x is the raw score.
m is the mean raw score.
s is the standard deviation.

for the first problem:

x = 12
m = 42
s = 12

z = (12 - 42) / 12 = 30 / 12 = -2.5

from the z-score tables, the area under the distribution curve to the left of a z-score of -2.5 will be .0062 = .62%.

same answer.

z-score table used can be found at:

http://www.stat.ufl.edu/~athienit/Tables/Ztable.pdf

use of the lane normal distribution calculator will provide the same result as shown below:

$$$

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