Answer to Question #202514 in Statistics and Probability for Isayad

Question

From the previous data it is known that the length of time between customer complaints against a particular product (in months) is a gamma distribution with a 2 and 4. Changes are made. to tighten quality control requirements. After this change, 20 months passed before the first complaint. Does the tightening of quality control appear to be effective?

Answer 1

For a gamma distribution expected value:

$E(X)=k\theta$

we have:

$k=2,\theta=4$

Then:

$E(X)=2\cdot4=8$ months

So, we can conclude that quality control is effective, because after changes the length of time between customer complaints is much more than the expected value.