An anthropologist wishes to estimate the average height of the inhabitants of a certain region. If the population standard deviation is assumed to be 2.5 inches and if she randomly samples 100 people, find the probability that the difference between the sample mean and the true population mean will not exceed 0.5 inches. If the anthropologist wants the difference between the sample mean and the population to be less than 0.4 inches with probability 95%, what sample size should she use?

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