Exerclse $8-27($Algo$)($LO$8-3)$

Suppose your statistics instructor gave six examinations during the semester. You received the following exam scores $($percent correct$)$: $93,67,88,90,89,$ and $72.$ The instructor decided to randomly select two exam scores, compute their mean, and use this score to determine your final course grade.

a$.$ Compute the population mean. This is your average grade based on alf of your grades. $($Round your answer to $2$ decimol places.$)$

Population mean

b$.$ Compute the population standard deviation. $($Round your onswer to $2$ declmal pleces.$)$

Population standard deviation

c$.$ How many different scores could be calculated if your instructor decided to random sample two of your exam scores?

Number of different samples

d$.$ List all possible samples of size $2$ and compute the mean of each. $($Round your mean answers ro $1$ decimal ploce.$)$

$\backslash$table$[[$Sample$,$Values,Sum,Mean$],[1,,,],[2,,,],[3,,,],[4,,,],[5,,,],[6,,,],[7,,,],[8,,,],[8,,,],[10,,,],[11,,,],[12,,,],[13,,,],[14,,,],[15,,,]]$

e$.$ Compute the mean of the sample means and the standard error of the sample means. $($Round your answers $802$ decimal pleces.$)$

$\backslash$table$[[$Mean of the sample means,$83\mathrm{.}17],[$Standard error of the sample means,$]]$

Applying the central limit theorem, if the instructor randomly samples two of your exam scores to compute an average as your final course grade, what is the probability your final course grade will be less than $83\mathrm{.}17?$ What is the probability that your final course grade will be more than $83\mathrm{.}17?($Round your onswers to $1$ decimal pleces.$)$

$\backslash$table$[[,$Probability$],[$Final course grade will be more then $83\mathrm{.}17,0\mathrm{.}5],[$Final course grade will be less than $83\mathrm{.}17,0\mathrm{.}5]]$