CPM Homework Help : INT3 Problem 6-44

A survey of $80$ seniors at Algieres High School finds that $65\%$ have been accepted to a four-year university. A computer simulation is conducted and the proportions sorted to determine the sample-to-sample variability:

Proportion of students accepted to a four-year university (sorted).
Simulation mean $= 0.65$ .

$0.51$
$0.52$
$0.54$
$0.54$
$0.56$

$0.56$
$0.56$
$0.57$
$0.57$
$0.58$

$0.58$
$0.59$
$0.59$
$0.59$
$0.59$

$0.59$
$0.59$
$0.59$
$0.60$
$0.60$

$0.60$
$0.61$
$0.61$
$0.61$
$0.61$

$0.61$
$0.62$
$0.62$
$0.62$
$0.62$

$0.62$
$0.62$
$0.62$
$0.62$
$0.62$

$0.62$
$0.63$
$0.63$
$0.63$
$0.63$

$0.63$
$0.63$
$0.63$
$0.63$
$0.63$

$0.64$
$0.64$
$0.64$
$0.64$
$0.65$

$0.65$
$0.65$
$0.65$
$0.65$
$0.65$

$0.65$
$0.65$
$0.65$
$0.65$
$0.66$

$0.66$
$0.66$
$0.66$
$0.67$
$0.67$

$0.67$
$0.67$
$0.67$
$0.67$
$0.67$

$0.67$
$0.67$
$0.68$
$0.68$
$0.68$

$0.68$
$0.68$
$0.68$
$0.69$
$0.69$

$0.69$
$0.70$
$0.70$
$0.71$
$0.71$

$0.71$
$0.71$
$0.71$
$0.71$
$0.72$

$0.73$
$0.73$
$0.73$
$0.73$
$0.74$

$0.74$
$0.75$
$0.76$
$0.76$
$0.77$

checksum $64.64$

Use the technique in problem 6-42 to determine the upper and lower $5\%$ bounds of the sample-to-sample variability.
Hint (a):
The simulation was run $100$ times.
Which results represent the $5$ th and $95$ th percentiles?
Predict the proportion of the seniors at Algieres High who have been accepted to a four-year university and give the margin of error.
Hint (b):
The mean (center) is $\approx65\%$ .
Acceptance rates can be expected to be in the range of your answers to part (a).
Express this as $65\%$ $\pm x\%$ .