Assessing the Unusualness of a Sample Mean Using the Central Limit Theorem

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Assessing the Unusualness of a Sample Mean Using the Central Limit Theorem Assume that a population is normally distributed with a mean of 100 and a standard deviation of 15. Would it be unusual for the mean of a sample of 3 to be 115 or more? Why or why not? Solution: Let X be the sample mean of size 3. Given the population mean #=100 and standard deviation o=15. By the Central Limit Theorem, Xx follows a normal distribution with mean x; =100 and standard deviation of oz =F =1%=8.66. So, the probability of getting sample mean to be 115 or more is P(X 2115) = 1- P(X <115) Let Zz =21% Then Z follows the standard normal distribution N(O, 1). So,
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