The Bright Idea Lighting Company wants to determine what proportion of LED flashlights that come off of its assembly line are defective. It takes many samples of $100$ flashlights over the week and determines the proportion that are defective in each sample. The results of their tests as shown below:

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

   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):

   When the data is sorted, these are the $5$th and $95$th items on the list.

   Answer (b):

   $0.11$ and $0.05$

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.