Sections 5.3-4

#37. a) Your first job is to determine all of the possible values for X-bar, and then calculate the probability for each value. For example, X-bar could be 25.0, but only if X_{1} = 25.0 and X_{2} = 25.0, and that happens with probability 0.04. so one value of X-bar is 25.0, with probability 0.04. X-bar could also be 32.5, but that only happens if X_{1} = 25.0 and X_{2} = 40.0, or X_{1} = 40.0 and X_{2} = 25.0. So the probability is 0.10 + 0.10 = 0.20. There are four more possible values for X-bar.

After you have all the values and probs for X-bar, then you can find the mean of the pdf by calculating E(X-bar) = Σ(X-bar)*Prob(X-bar)

#46. Remember that X-bar has a ?D(μ_{pop}, σ/sqrt(n)) distribution. Use that to answer the questions.

#47. Convert the problem to a z-score question, then use the z-table.

#49. The question is about the total time to sequentially grade 40 papers, i.e. ΣX_{i}, where the X_{i}'s refer to the times it takes to grade the individual papers. Translate that question to one about the
the **average** time to grade 40 papers

#50. On your own on this one.