Question: Suppose that X; are IID normal random variables with mean 6 and variance 7, for i = 1, 2, ..., n. (a) Calculate P(X1

Suppose that X; are IID normal random variables with mean 6 and

Suppose that X; are IID normal random variables with mean 6 and variance 7, for i = 1, 2, ..., n. (a) Calculate P(X1 < 6.8), i.e., the probability that the first value collected is less than 6.8. (b) Suppose we collect a sample of size 2, X1 and X2. What is the probability that their sample mean is greater than 5.6? (c) Again, suppose we collect two samples (n=2), X1 and X2. What is the probability that their sum is greater than 12.5? (Hint: P(X1 + X2 12.5) = P(X > 6.25). (d) Suppose we collect a sample size of n=100. What is the probability that the sample mean is between 5.6 and 6.26?

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