The Bright Idea Lighting Company wants to determine what proportion of LED flashlights that come off of its assembly line are defective. A quality engineer takes many samples of $100$ flashlights over the week and determines the proportion that are defective in each sample. The results of the tests have been ordered from low to high and are shown below:

1. What is the mean proportion of defective flashlights (as a percentage)?

   Hint (a):

   The sum of the data is $7.83$ and there are $100$ samples.

2. What are the upper and lower $5\%$ bounds of the sample-to-sample variability?

   Hint (b):

   These are the average of the $5$th and $6$th items and the average of the $95$th and $96$th items on the list.

   Answer (b):

   $0.05$ and $0.11$

3. Predict the proportion of defective flashlights (in percent) in the whole population and give the margin of error.

   Answer (c):

   There is a $6\%$ different in the upper and lower bounds, therefore we predict $7.83\%$ $\pm3\%$ of the flashlights will be defective.