Home > INT3 > Chapter 6 > Lesson 6.2.2 > Problem6-44

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 $= 0.65$. $0.51$ $0.52$ $0.54$ $0.54$ $0.56$ $0.60$ $0.61$ $0.61$ $0.61$ $0.61$ $0.63$ $0.63$ $0.63$ $0.63$ $0.63$ $0.66$ $0.66$ $0.66$ $0.67$ $0.67$ $0.69$ $0.70$ $0.70$ $0.71$ $0.71$ $0.56$ $0.56$ $0.57$ $0.57$ $0.58$ $0.61$ $0.62$ $0.62$ $0.62$ $0.62$ $0.64$ $0.64$ $0.64$ $0.64$ $0.65$ $0.67$ $0.67$ $0.67$ $0.67$ $0.67$ $0.71$ $0.71$ $0.71$ $0.71$ $0.72$ $0.58$ $0.59$ $0.59$ $0.59$ $0.59$ $0.62$ $0.62$ $0.62$ $0.62$ $0.62$ $0.65$ $0.65$ $0.65$ $0.65$ $0.65$ $0.67$ $0.67$ $0.68$ $0.68$ $0.68$ $0.73$ $0.73$ $0.73$ $0.73$ $0.74$ $0.59$ $0.59$ $0.59$ $0.60$ $0.60$ $0.62$ $0.63$ $0.63$ $0.63$ $0.63$ $0.65$ $0.65$ $0.65$ $0.65$ $0.66$ $0.68$ $0.68$ $0.68$ $0.69$ $0.69$ $0.74$ $0.75$ $0.76$ $0.76$ $0.77$ checksum $64.64$
1. Use the technique in problem 6-42 to determine the upper and lower $5\%$ bounds of the sample-to-sample variability.

The simulation was run $100$ times.
Which results represent the $5$th and $95$th percentiles?

2. Predict the proportion of the seniors at Algieres High who have been accepted to a four-year university and give the margin of error.

The mean (center) is $\approx65\%$.
Acceptance rates can be expected to be in the range of your answers to part (a).
Express this as $65\%$ $\pm x\%$.