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Say that the annual profits of small businesses on Main Street follow a normal distribution with...

Say that the annual profits of small businesses on Main Street follow a normal distribution with unknown mean μ and unknown variance σ2. A random sample of 6 businesses on Main Street is taken where Xi denotes annual profits of a sample member i. Eventually a seventh business is selected for the study. This business is independent of the other businesses in the area. Can we say that the distribution of X_7 ∼ N(μ, σ2)? Why or why not?

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Answer #1

Yes, as X7 is independent and identically distributed

X7 should also follow N(mu,sigma^2)

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