2. Al pharmaceutical company employs sales representatives (\"sales reps\") who makes visits or calls to dillerent doctors7 ofces every month to promote a particular drug of the company. The number of prescriptions X that each sales representative generates each month is an uncertain quantity. Based on historical data, the pharmaceutical company models X using the following distribution: {DOD-JO'JUIHRMMb'D P O Oh - ,_.,_.,_. [Obto PPP DOD DOD ,_i,_i,g_ Answer the following questions: (a) What is the probability that a sales rep will generate at least 8 prescriptions in a month? (b) What is the probability that a sales rep will generate 7 or fewer prescriptions in a month? C What is the Irobability that a sales I9 ) Wlll enerate at least 3 and at H1061: 6 rescri thDS in g P P a month? (d) Find the expected value of X. (e) Find the variance and standard deviation of X. Suppose that the pharmaceutical company is considering the following bonus payment scheme. For each prescription, a sales rep will receive a payment of $750. Based on this information, answer questions (f) and (g) below. (f) What is the probability that a sales rep will receive a total bonus payment of $4500 or more in a month? (g) What are the expected value and standard deviation of the total bonus payment that a sales rep will receive? Instead of the bonus payment policy described above, the company considers the following alternate scheme: I For the rst 3 prescriptions, the rep will receive a payment of $500 per prescription: I For the next 4 prescriptions, the rep Will receive a payment of $750 per prescription; and I For every prescription above 7 prescriptions, the rep will receive a payment of $1000 per pre scription For example, if a rep generates 5 prescriptions, they will be paid 3 x $500 + (5 7 3) x $750 : $3000. As another example, if they generate Q prescriptions, they will be paid 3 x $500 + 4 x $750 + (9 7 7) X $1000 : $6500. Using this information, answer question (h) below. (h) What is the expected value of the total bonus payment