Question

Suppose x has a distribution with μ = 11 and σ = 9. (a) If a...

Suppose x has a distribution with μ = 11 and σ = 9.

(a) If a random sample of size n = 48 is drawn, find μx, σ x and P(11 ≤ x ≤ 13). (Round σx to two decimal places and the probability to four decimal places.)

μx =

σ x =

P(11 ≤ x (x bar) ≤ 13) =

(b) If a random sample of size n = 63 is drawn, find μx, σ x and P(11 ≤ x ≤ 13). (Round σ x to two decimal places and the probability to four decimal places.)

μx =

σ x =

P(11 ≤ x ≤ 13) =

(c) Why should you expect the probability of part (b) to be higher than that of part (a)? (Hint: Consider the standard deviations in parts (a) and (b).) The standard deviation of part (b) is ______ part (a) because of the _____ sample size. Therefore, the distribution about μx is ______ .

*** the probability (11< x < 13) has x bar in the middle

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