Question 210:

Asked on May 29, 2008

Tags: Z-Score

1

Answer:

No answer provided yet.

The mean is 100g with standard deviation of 5g. You have a target mean of 106 grams, so to generate the z-score subtract the mean from the target and divide by the standard deviation=

( 106-100 ) / 5 = 1.2. While the machine will over-fill and under-fill some bags, we're only interested in seeing what percent of customers will get short-changes (b/c no one complains about getting too much for their money!). We then are only concerned with the area below 100 grams. Using the z-score to percentile calculator and entering 1.2 and selecting 1-sided area we get about 11% of customers will get less than 100g of coffee.

It might also help to visualize this. Go to the interactive graph of the standard normal curve , enter the mean of 100 and SD of 5 then hover over the graph for a z-score of -1.2 or 1.2 to see the shaded or white area (which should be around 11%).