The amount of time required for a mechanic to replace a clutch is normally distributed with mean 100 minutes and standard deviation of 20 minutes. A car is taken to the mechanic to have its clutch replaced. Let X be the number of minutes it takes to repair the car, and Z be the standard normal distribution. (a) Calculate the z-value corresponding to X = 120.
The amount of time required for a mechanic to replace a clutch is normally distributed with mean 100 minutes and standard deviation of 20 minutes. A car is taken to the mechanic to have its clutch replaced. Let X be the number of minutes it takes to repair the car, and Z be the standard normal distribution. (a) Calculate the z-value corresponding to X = 120.
A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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Transcribed Image Text:4. The amount of time required for a mechanic to replace a clutch is
normally distributed with mean 100 minutes and standard deviation
of 20 minutes. A car is taken to the mechanic to have its clutch
replaced. Let X be the number of minutes it takes to repair the car,
and Z be the standard normal distribution.
(a) Calculate the z-value corresponding to X
120.
(b) Hence or otherwise find the probability that the car will be ready
in two hours or less.
(c) Find the probability that the car will not be ready until after 90
minutes.
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