Question

Question 3:

Federal regulations state that the net contents of packaged goods must match or exceed the amount shown on the labels – for example, if the food packaging says it contains 4 oz of food, the package must contain at least 4 oz in order to be compliance with federal regulations. As a quality engineer, you determine that a quality issue has caused you to produce 15 cases of underweight product out the 120 cases produced in that shift. Unfortunately, your company’s distribution department has already shipped 40 of these cases. Use this formation to answer the following question.

you would like to know how many of the underweight t cases have been shipped. How you would define your random variable?

X = number of cases that have been shipped

X = number of underweight cases that have been shipped

X = number of underweight cases from produced

X = number of underweight cases from 15 underweight cases of products that have been shipped

What is the random variable’s distribution that you defined in question 3a?

Answer 1

Given that distribution department has already shipped 40 cases, and we want to know how many of the underweight cases have been shipped. Let X denotes this, that is X is the random variable which denotes the number of underweight cases that have been shipped. So X can take values 0, 1, 2...40.

Ie, if there is possibility that no underweight case is shipped so X=0, and if all the products shipped are underweight then X=40

Given that a quality issue is caused when you produce 15 cases of underweight product out of 120,  

Then probability of getting an underweight case is 15/120

So Here X follows a binomial distribution since number of trails is fixed, 40 and probability of success is not changing in trials

So X follows binomial distribution with n= 40 and p=15/120