Let Y1, Y2, , Yn be independent, normal random variables, each with mean μ and variance...

Question

Question

Let Y1, Y2, , Yn be independent, normal random variables, each with mean μ and variance σ^2.

(a) Find the density function of Yi i=1

f_Y(u) =

(b) If σ^2 = 25 and n = 9, what is the probability that the sample mean, Y, takes on a value that is within one unit of the population mean, μ?

That is, find P(|Y − μ| ≤ 1). (Round your answer to four decimal places.)

P(|Y − μ| ≤ 1) =

(c) If σ^2 = 25, find P(|Y − μ| ≤ 1) if n = 49, n = 64, and n = 81. (Round your answers to four decimal places.)

n = 49 P(|Y − μ| ≤ 1) =

n = 64 P(|Y − μ| ≤ 1) =

n = 81 P(|Y − μ| ≤ 1) =

Answer 1

Answer #1

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Answer 2

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