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Independent random samples of n = 100 observations each are drawn from normal populations. The parameters...

Independent random samples of n = 100 observations each are drawn from normal populations. The parameters of these populations are:

• Population 1: μ1 = 300 and σ1 = 60;

• Population 2: μ2 = 290 and σ2 = 80.

(1) What is the probability that the mean of Population 1 is between 294 and 306?
(2) How many samples should be included if we want the probability in Part (1) to be at least 95%?   (3) What is the probability that the mean of Population 1 is greater than the mean of Population 2?

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