The length of time to perform an oil change at a certain shop is normally distributed with mean 29.5 minutes and standard deviation 3 minutes. What is the probability that a mechanic can complete 16 oil changes in an eight-hour day?
What will be an ideal response?
Let 
be the times needed to complete 16 oil changes.
Let 
be the total time needed to complete all 16 oil changes.
Then T is normally distributed with mean 
and standard deviation 
.
The mechanic completes 16 oil changes in an eight-hour day if T < 480.
The z-score of 480 is
The area to the left of z=0.97 is 0.7486.
P(T<480) = 0.7486.
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