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a. X is distributed as a Normal random variable, with a mean of 100 and a...

a. X is distributed as a Normal random variable, with a mean of 100 and a standard deviation of 20. You're considering taking a random sample of 1000 Xs, and calculating the sample mean Xbar. Of course, different random samples would give you different numbers. What is the standard deviation of all of the possible different Xbars you could have calculated? (Please report your answer to two decimal places, such as 5.67.)

b. X is distributed as a Normal random variable, with a mean of 100 and a standard deviation of 20. You're considering taking a random sample of two Xs (a really small sample) and calculating the sample mean Xbar. Of course, different random samples would give you different numbers. What is the standard deviation of all of the possible different Xbars you could have calculated? (Please report your answer to two decimal places, such as 5.67.)

c. X is distributed as a Normal random variable with mean of 150 and a standard deviation of 10 (i.e X~N(150,10). You take a random sample of 20 items from X and you calculate the average of this sample. What is the expected value of this sample average? (i.e. what value would you expect to get for the average of this small sample?)

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