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| Math Central | Quandaries & Queries |
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Question from jude, a parent: Regarding the time it takes for an oil change has a normal distribution with a mean of 17.8 minutes and std. deviation of 5.2 minutes. A free oil change will be given to any customer that must wait beyond the guaranteed time. If they don't want to give more than 1% of its customers free oil changes how long should the guarantee be (to the nearest minute). Thank you. |
Jude,
Your textbook will have a table of the probability that a standardized normal distribution ("Z") is less than a certain value. This is also the probability that any normal random variable is less than that many standard deviations above the mean. (You can get the same information from books of math tables, a scientific calculator, or online at various places.) So if you find a value (say 0.7) in the body of the table, look on the margin and you find that it corresponds to a value of about 0.5. Interpret that as saying that a normal RV will be less than half a standard deviation above the mean 70% of the time.
They want 99% of the times to be less than the cutoff. How many standard deviations above the mean is that?
Now, what's that in minutes, using the figures form your problem?
Good Hunting!
RD
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