2.(3 points) LetY₁, Y₂, ...Y₂₅denote a random sample of 25 normal random variables, each identically distributed with mean= 61 and variance= 900

a.(0.5 points) Calculate the estimated probability of one of these random variables having an observed value that exceeds 94.

b.(0.5 points) What is the sampling distribution of the sample mean? Please comment on this distribution, in particular its mean and standard error.

c.(1 point) Calculate the estimated probability of the sample meanexceeding 94. Is this estimated probability larger or smaller than the answer from part a.)? Why do you think you obtained this result?

d.(1 point) Compare and contrast the standard deviation from the standard error.