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Category: Calculus and Above
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Experience:  B.S. in Civil Engineering
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# The MPG (***** ***** per gallon) certain compact car is

### Customer Question

The MPG (***** ***** per gallon) for a certain compact car is normally distributed with a mean of 31 and a standard deviation of 0.8. What is the probability that the MPG for a randomly selected compact car would be less than 32?
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Submitted: 1 year ago.
Category: Calculus and Above
Expert:  Ryan replied 1 year ago.

Hi,

Thank you for using the site. I'll have a solution posted for you shortly.

Ryan

Expert:  Ryan replied 1 year ago.

Since the population standard deviation is known, use the z-statistic.

z = (x - µ) / sigma = (32 - 31) / 0.8 = 1.25

Then, using a statistical calculator, or a table of the normal distribution:

P(x < 32) = P(z < 1.25) = 0.8944

Thus, the probability that a randomly selected compact car will have an MPG which is less than 32 is 0.8944.