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11-42.
  1. 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: Homework Help ✎

    Proportion of defective flashlights in 100 samples

    0.02
    0.04
    0.05
    0.05
    0.05

    0.06
    0.06
    0.06
    0.06
    0.06

    0.07
    0.07
    0.08
    0.08
    0.08

    0.08
    0.09
    0.09
    0.09
    0.09

    0.09
    0.10
    0.10
    0.10
    0.10

    0.05
    0.05
    0.05
    0.05
    0.05

    0.06
    0.06
    0.07
    0.07
    0.07

    0.08
    0.08
    0.08
    0.08
    0.08

    0.09
    0.09
    0.09
    0.09
    0.09

    0.10
    0.10
    0.10
    0.10
    0.10

    0.05
    0.05
    0.05
    0.05
    0.06

    0.07
    0.07
    0.07
    0.07
    0.07

    0.08
    0.08
    0.08
    0.08
    0.08

    0.09
    0.09
    0.09
    0.09
    0.09

    0.10
    0.10
    0.11
    0.11
    0.11

    0.06
    0.06
    0.06
    0.06
    0.06

    0.07
    0.07
    0.07
    0.07
    0.07

    0.08
    0.08
    0.08
    0.08
    0.08

    0.09
    0.09
    0.09
    0.09
    0.09

    0.11
    0.11
    0.12
    0.12
    0.13

    checksum 7.83

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

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

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

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

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

0.11 and 0.05

There is a 6% different in the upper and lower bounds, therefore we predict 7.83% ± 3% of the flashlights will be defective.