### Home > INT3 > Chapter 6 > Lesson 6.2.1 > Problem6-35

6-35.

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:

 Proportion of defective flashlights in $100$ samples $0.02$ $0.04$ $0.05$ $0.05$ $0.05$$0.05$ $0.05$ $0.05$ $0.05$ $0.05$$0.05$ $0.05$ $0.05$ $0.05$ $0.06$$0.06$ $0.06$ $0.06$ $0.06$ $0.06$ $0.06$ $0.06$ $0.06$ $0.06$ $0.06$$0.06$ $0.06$ $0.07$ $0.07$ $0.07$$0.07$ $0.07$ $0.07$ $0.07$ $0.07$$0.07$ $0.07$ $0.07$ $0.07$ $0.07$ $0.07$ $0.07$ $0.08$ $0.08$ $0.08$$0.08$ $0.08$ $0.08$ $0.08$ $0.08$$0.08$ $0.08$ $0.08$ $0.08$ $0.08$$0.08$ $0.08$ $0.08$ $0.08$ $0.08$ $0.08$ $0.09$ $0.09$ $0.09$ $0.09$$0.09$ $0.09$ $0.09$ $0.09$ $0.09$$0.09$ $0.09$ $0.09$ $0.09$ $0.09$$0.09$ $0.09$ $0.09$ $0.09$ $0.09$ $0.09$ $0.10$ $0.10$ $0.10$ $0.10$$0.10$ $0.10$ $0.10$ $0.10$ $0.10$$0.10$ $0.10$ $0.11$ $0.11$ $0.11$$0.11$ $0.11$ $0.12$ $0.12$ $0.13$ checksum $7.83$
1. What is the mean proportion of defective flashlights (as a percentage)?

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?

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.

$0.05$ and $0.11$

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

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