Suppose you are a travel agent. A broker approaches you and offers to pay you a
ID: 3128520 • Letter: S
Question
Suppose you are a travel agent. A broker approaches you and offers to pay you a certain amount of money for organizing events for bus trips the broker advertises. The broker guarantees that you can book 10 buses every month. There are two types of bus trips: Economy and Premium. The broker cannot predict with certainty how many of each bus types there will be, but tells you to expect that on average 1 in 5 buses will be premium buses. Please answer the following questions: 1) Show the probability model for this distribution. 2P 2) What is the expected value for the number of premium buses per month? 1P 3) What is the variance of the number of premium buses per month? 1P 4) What is the probability of the broker sending you 6 or more premium buses per month? 1P The agreement with the broker also stipulates that you will receive a certain amount of revenue for organizing the events. This amount varies by bus type: you receive $1000 per bus for economy buses and $1500 per bus for premium buses. 5) What are the minimum and maximum amounts you can earn per month? 1P 6) What is the expected value for your monthly revenues from this broker? 1P 7) What is the standard deviation of your monthly revenues from this broker? 1P You decide that you are interested and arrange for a trial period with the broker. The trial period is a great success, and the broker tells you that they would be interested in increasing the number of buses per month. You calculate two scenarios: 20 buses per month and 30 buses per month; with revenues per bus and the ratio of economy to premium buses remaining the same as before. 8) What are the expected value of the number of premium buses for the scenario of 20 buses and the scenario of 30 buses? 2P 9) What are the variances of the number of premium buses for the scenario of 20 buses and the scenario of 30 buses? 2P 10) What are the expected values for your revenues from the two scenarios? 2P 11) What are the standard deviations for your revenues from the two scenarios? 2P 12) What are the coefficients of variation for the two scenarios? 2P
Explanation / Answer
1) Show the probability model for this distribution.2P
The probability of a premium bus =1/5 ; total number of buses (trials) =10
Let X be the number of premium buses, X follows binomial distribution with n,p are
B(10,1/5)
2) What is the expected value for the number of premium buses per month? 1P
The expected number of premium buses per month = np =10*(1/5) =2
3) What is the variance of the number of premium buses per month? 1P
Variance = npq =2*(4/5)=8/5 =1.6
4) What is the probability of the broker sending you 6 or more premium buses per month? 1P
P(X>=6) = 1-P(X<=5) = 1-0.993630618=0.006369382
5) What are the minimum and maximum amounts you can earn per month? 1P
Minimum amount earn =10*$1000=$10,000
Please dont ask too many questions in a single post
Maximum amount ear= 10*$1500 =$15,000