Calculus and Above
Calculus Questions? Ask a Mathematician for Answers ASAP
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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.
Please feel free to ask if you have any questions about this solution.