2) (.8 pts each) Which family of distributions covered in class would you use to model the following descriptions of random variables? A company plans to release a popular new smart phone. According to their projections, each day, sales of the phone will be some proportion of the prior day's. All of these proportions are independent and identically distributed. What sort of distribution would you use to model sales on day 50? b. A factory is using an obsolete machine with a known defect: once it starts running, one of its parts may break down suddenly at any time, however the part will appear to be as good as new until it finally breaks. Fortunately, the factory has four spares of the part on hand . Unfortunately , once they run out of spares they won't be able to replace the part, and will have to order a new model. What sort of distribution would you use to model the time until the machine needs to be replaced? c. A sales office decides to try out a new incentive program. At the end of each month, the employee with the best sales number will get to spin a wheel, marked from $100 to $1,000 in increments of $100. Each number is equally likely to come up. The employee is paid that amount as a bonus. What sort of distribution would you use to model the money paid to the employee ? d. A farm produces caviar and employs a taster to grade it. Each batch has a 15% of being deemed the highest grade. One week, they produce 30 batches of caviar. What is the distribution of the number of batches awarded the highest grade? . A company is trying to predict their legal fees after a copyright claim is filed against them. The law firm they hire is unsure exactly how much they're going to bill, but they quote a minimum, most likely, and maximum amount. What distribution should they use to estimate their fees