Question 1143105
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.