SOLUTION: A dishwasher has a mean life of 12 years with an estimated standard deviation of 1.25 years ("Appliance life expectancy," 2013). Assume the life of a dishwasher is normally distri

Question 1143105: A dishwasher has a mean life of 12 years with an estimated standard deviation of 1.25 years ("Appliance life expectancy," 2013). Assume the life of a dishwasher is normally distributed.
Using Excel I entered this:
I am using Excel. An online calculator gives me the answer of 0.054112 and Excel says 0.05548
d. Find the probability that a dishwasher will last between 8 and 10 years. =SUM(NORM.DIST(10,12,1.25,TRUE)+NORM.DIST(8,12,1.25,TRUE))
How do I know which is correct?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
i'm not sure how you got the area of .054112 or .05548.
what was the problem that lead you to those answers?

the probability that the dishwasher would last between 8 and 10 years should be the area to the left of the z-score associated with the raw score of 10 minus the area to the left of the z-score associated with the raw score of 8.

your z-scores would be:

(10 - 12) / 1.25 = -1.6
(8 - 12) / 1.25 = -3.2

the area to the left of a z-score of -1.6 = .0547992894
the area to the left of a z-score of -3.2 = .006872020803

the area in between = .0547992894 - .006872020803 = .0541120873

your formula in excel was:

=SUM(NORM.DIST(10,12,1.25,TRUE)+NORM.DIST(8,12,1.25,TRUE))

it should have been:

=NORM.DIST(10,12,1.25,TRUE) - NORM.DIST(8,12,1.25,TRUE)

to get the area between 2 z-scores, you subtract the smaller area from the larger area.

put another way, you subtract the area to the left of the less positive z-score from the area to the left of the higher z-score.

you added the areas together using the sum function which gave you the wrong answer.

RELATED QUESTIONS
A manufacturer finds the life expectancy of a dishwasher to be 11 years. The standard... (answered by stanbon)

According to the historical data, the life expectancy in Belgium is less than the life... (answered by ikleyn)

The mean life of an appliance manufactured by your company is 10 years with a standard... (answered by jim_thompson5910)

The lifetime of a certain appliance is normally distributed with a mean life of 6.5... (answered by Fombitz)

Suppose the age at death for politicians can be modeled by an approximately normal... (answered by Boreal)

According to the historical data, the life expectancy in the United States is equal to... (answered by rothauserc)

The life expectancy of a circulating coin is 2020 years. The life expectancy of a... (answered by ikleyn)

Please help Records of individuals from France who died recently are selected at... (answered by stanbon)