QA 233 (Basic Business Statistics)

Practice Problems VI - Chapter 6

Hello QA 233 students! The following problems require you to use material from 'Continuous Probability Distributions'  (slide set 6 and chapter 6 in the ASW textbook). I have also posted the solutions on the Virtual Classroom web page. Have a good day.

Marsha Mallo is a Quality Assurance Technician for Pillar Foods, Inc., producers of Choco-Poofies. Ms. Mallo is primarily responsible for ascertaining that the popular children’s breakfast cereal contains the desired quantity of chocolate candy pieces. The chocolate candy pieces are far more expensive than the oat cereal pieces they are mixed with to produce Choco-Poofies, so Pillar Foods does not want the amount of chocolate candies in each box of Choco-Poofies to be too high (i.e., the producer’s risk). On the other hand, the chocolate candies are what makes Choco-Poofies popular with children, so Pillar Foods also does not want the amount of chocolate candies in each box of Choco-Poofies to be too low (i.e., the consumer’s risk). In response to these two concerns, Pillar Foods has decided that their most popular sized box of Choco-Poofies (the thirty-six ounce economy size) should contain a mean of twelve ounces of chocolate pieces. Furthermore, they have also decided that the variance in the amount of chocolate pieces contained in a thirty-six ounce box of Choco-Poofies should be 1.96. In reviewing the historical production data, Marsha has found that the amount of chocolate candies in thirty-six ounce boxes of Choco-Poofies to be normally distributed.

1. Suppose a financial analyst at Pillar Foods has determined that Pillar will loose money on a thirty-six ounce box of Choco-Poofies if it contains more than fourteen ounces of chocolate candies. Help Marsha determine the probability that a randomly selected thirty-six ounce box of Choco-Poofies will expose Pillar to the producer’s risk. In other words, what is the probability that Pillar will loose money on a box of Choco-Poofies due to overfill of chocolate candies if the production process is working at the target levels (a mean of twelve ounces and a variance of 1.96) set by Pillar?

2. Suppose a marketing analyst at Pillar Foods has determined that Pillar risks loosing a youthful customer of Choco-Poofies if a thirty-six ounce box contains less than eleven ounces of chocolate candies. Help Marsha determine the probability that a randomly selected thirty-six ounce box of Choco-Poofies will expose Pillar to the consumer’s risk. In other words, what is the probability that a thirty-six ounce box of Choco-Poofies will put Pillar at risk of loosing a customer if the production process is working at the target levels (a mean of twelve ounces and a variance of 1.96) set by Pillar?

3. If the production process is working at the target levels (a mean of twelve ounces and a variance of 1.96) set by Pillar, what is the probability that a randomly selected thirty-six ounce box of Choco-Poofies will expose Pillar to either the producer’s risk or the consumer’s risk? What is the probability that a randomly selected thirty-six ounce box of Choco-Poofies will expose Pillar to neither the producer’s risk or the consumer’s risk?

Return to the List of Practice Problem Sets