# Thread: probability of consumption

1. ## probability of consumption

could someone let me know what i'm doing wrong?

A study of the amount of time it takes a mechanic to rebuild the transmission for a 1992 Chevrolet Cavalier shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics are randomly selected, find the probability that their mean rebuild time exceeds 8.1 hours.

mu (sample) = mu = 8.4
s.d. (sample) = 1.8/ sq. rt. 40
P( greater than 8.1) = (8.1-8.4)/(1.8/ sq. rt. 40)

i'm given a choice of four answers and this one definitely isn't one of them, ty.

2. What answers are you given?

Peter

3. a. 0.8531
b. 0.7285
c. 0.8457
d. 0.9416

4. Rzum,

The answer is a) 0.8531 and I now realise what went wrong (I think that you read the area to the left of -1.05):

Let x be the mean time for the 40 mechanics

Standardize the mechanics: (8.1-8.4)/(1.8/ sq. rt. 40) = -1.05 = Z

P( x > 8.1) = P(Z > -1.05), this means the area to the right of Z = -1.05.

Greater than means to the right and less than means to the left.

If you were asked to find the probability that their mean rebuild time is less than 8.1 hours you would look up the area to the left of -1.05 which is 0.1469, I think this is what you did.

HTH
Peter

5. That helped a lot, thanks!

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