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.
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