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q04_sol - ISyE 2028A Summer 2010 1 Let X 1 X n be a random...

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ISyE 2028A, Summer 2010 Friday June 18 Quiz 4 Solutions 1. Let 1 , , n X X  be a random sample from a population having a mean µ and standard deviation σ . Provided that n is large, the Central Limit Theorem (CLT) implies that X is __________ distributed. [2 points] ANSWER: ( approximately) normally 2. When X is the mean of a random sample of size n ( n is small) from a normal population with mean µ , the random variable ( ) /( / ) T X S n µ = has a probability distribution called t -distribution with __________. [2 points] ANSWER: n-1 degrees of freedom 3. Let t ν denote the density function curve for a t -distribution with ν degrees of freedom. As ν increases, the t-distribution converges to __________ (what distribution?).
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