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The Central Limit Theorem

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Sampling Distribution and the Central Limit Theorem

Find the probabilities.

a. From National Weather Service records, the annual snowfall in the TopKick Mountains has a mean of 92 inches and a standard deviation ? of 12 inches. If the snowfall from 25 randomly selected years are chosen, what it the probability that the snowfall would be less than 95 inches?

b. The loan officer rates applicants for credit. Ratings are normally distributed. The mean is 240 and the standard deviation is 60. If 36 applicants are randomly chosen, what is the probability that they will have a rating between 230 and 260?

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Solution Summary

Step by step method for computing probability based on central limit theorem is given in the answer.

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Sampling Methods and the Central Limit Theorem

A recent study by the Greater Los Angeles Taxi Drivers Association showed that the mean fare charged for service from Hermosa Beach to LA International Airport is $18 and the standard deviation is $3.50. We select a sample of 15 fares.
a. What is the likelihood that the sample mean is between $17 and $20?
b. What must you assume to make the above calculation?

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