Suppose x has a distribution with μ = 11 and σ = 3. (a) If a...

Suppose x has a distribution with μ = 11 and σ = 3.

(a) If a random sample of size n = 39 is drawn, find μ_x, σ_x and P(11 ≤ x ≤ 13). (Round σ_x to two decimal places and the probability to four decimal places.)

μ_x =

σ_x =

P(11 ≤ x ≤ 13) =

(b) If a random sample of size n = 66 is drawn, find μ_x, σ_x and P(11 ≤ x ≤ 13). (Round σ_x to two decimal places and the probability to four decimal places.)

μ_x =

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 μ_x is .

Expert Solution

orchestra answered 2 years ago

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