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Discuss Validity of Central Limit Theorem

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What is the Central Limit Theorem? How large should the sample size be if the underlying distribution of the population values are:

a. Normally distributed (discuss).

b. Non-normally distributed. (discuss)

2. What is the difference, if any, between the standard deviation of the sample and the standard error of the mean? Discuss

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1. Central limit theorem is stated as follows: If a random sample of n observations is selected from a population, then when n is sufficiently large, the sampling ...

Solution Summary

The solution gives detailed analysis on validity of Central Limit Theorem and difference between the standard deviation of the sample and the standard error of the mean.

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The mean amount purchased by a typical customer at Churchill's Grocery Store is $23.50 with a standard deviation of $5.00. Assume the distribution of amounts purchased follows the normal distribution. For a sample of 50 customers, answer the following questions.
a. What is the likelihood the sample mean is at least $25.00?
b. What is the likelihood the sample mean is greater than $22.50 but less than $25.00?
c. Within what limits will 90 percent of the sample means occur

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