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 are defective The ###probability that less than 4 samples are defecti the ### sum of probabilities x0- x3 and equals 98.41% ### ### The ###probability that between 2 and 5 samples are ### 0.2638 or 26.38% ### ### ### ### ### ### ### ### ### ### ### ### mples are defective is 18.86% amples are defective is nd equals 98.41% 0.9840985 nd 5 samples are defective is the sum of P(x2 to x5) and equals to