M2a: Random Variable Distributions Scenario Assignment Scenario Script Caption: Princess Foods Corporation purchases glass containers from China for the packaging of their highend soups. These shipments come to Princess Foods Corporation in skids that were transported across the Pacific Ocean in giant shipping containers. When glass jars are shipped internationally, a small degree of defects is inevitable. Liwei has negotiated a deal with the vendor that an overall defect rate of 5% is acceptable. If more than 5% of the jars on a given skid are defective, Princess Foods Corporation does not have to pay for that shipment. If the defects are greater than 5%, that shipment is returned (at the shipper's expense). Liwei: There's a possibility of an increase in demand and therefore production. Will we need more glass jars? Bonnie: Can you take a look? I've noticed that the work that you're doing here seems to take the guess work out of things and...I really respect that. I'd love to hear your thoughts. Assignment If 20 samples of product are randomly selected and tested, what is the probability of the following: 1. Exactly two samples are defective 2. Between two and five inclusive are defective 3. Less than four are defective Due Dates 11:59pm ET, Sunday. Grading Criteria and Guidelines Grading criteria and detailed instructions for submission of assignments are available on the course website. Binomial with n=20 and p=0.05 x P(X=X) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### The probability that exactly 2 samples The probability that less than 4 sampl The probability that between 2 and 5 exactly 2 samples are defective is 18.86% less than 4 samples are defective is 5.95% between 2 and 5 samples are defective is the sum of P(x2 to x5) and equals to: o x5) and equals to: 0.2638 or 26.38%