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Question 3:

A control system was installed to regulate the weight of potato chips dumped into bags in a packaging operation. Given samples of 15 bags drawn from the operation before and after the control system was installed, evaluate the success of the system. Do this by comparing the arithmetic mean and standard deviations before and after. The bags should be 200 g.

Samples before: 201, 205, 197, 185, 202, 207, 215, 220, 179, 201, 197, 221, 202, 200, 195

Samples after: 197, 202, 193, 210, 207, 195, 199, 202, 193, 195, 201, 201, 200, 189, 197

Answer :

Given samples of 15 bags drawn from the operation before and after the control system was installed. The bags should be 200 g.

We need to evaluate the success of the system by comparing the arithmetic mean and standard deviations before and after. Samples before

201, 205, 197, 185, 202, 207, 215, 220, 179,201, 197, 221, 202, 200, 195

Let’s calculate the mean and standard deviation for samples before, Mean of samples before

= Sum of values / Total number of values. Mean of samples before

= (201+205+197+185+202+207+215+220+179+201+197+221+202+200+195)/15.

Mean of samples before= 200.8.

Therefore, the mean weight before the control system was installed was 200.8 g.Now let's calculate the standard deviation for samples before. For this we need to use this formula [tex]\sqrt{\frac{\sum (x_i-\bar{x})^2}{n-1}}[/tex]Where, xi are the sample values, and n is the sample size.

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