Problem 1. Monthly orders for Tesla Cars for the last 100 months are as follows: 15 months got 30 orders, 35 months got 40 orders, 20 months got 75 orders, 10 months got 105 orders, 15 months got 112 orders, and 5 months got 150 orders.
1.1. Show the probability distribution of monthly orders received in a table format.
1.2. Show the probability distribution as a histogram.
1.3. Calculate the mean, variance, and standard deviation of number of monthly orders received.
Problem 2. Suppose that it costs $600000 per month to run the operations of thebusinessin problem # 1and that the selling price of the caris $121,000. Let Y represent a random variable that represents the monthlyrevenue of Tesla.
2.1. Express Y as a linear function of X.
2.2. Show the probability distribution of Y(in a table format).
2.3. Compute the mean, variance, and standard deviation of Y utilizing the formulas used in class when discussing the concept on "linear functions of a random variable."
Problem 3. The percentage of UP accounting undergraduates passing CPA exam on the first try is 20% (assume every accounting student takes the test). You randomly select 17 graduating accounting students and would like to know a few things about their prospects of passing the test. Assume binomial distribution to answer the following questions.
3.1. What is the probability that exactly 4 will pass the exam?
3.2. What is the probability that at least 8 will pass the exam?
3.3. What is the probability less than 7will pass the exam?
(cont.)
3.4. Calculate the mean, variance, and standard deviation of the number of people passing the exam in this sample?
3.5. Is binomial distribution a good model in this case? Explain.
Problem 4. Suppose that the average number of calls received by Soda Straw Customer Service is 40 per hour. Assume Poisson distribution to answer the following questions:
4.1. What is the probability that at least 5 calls will arrive in a ten-minute period?
4.2. What is the probability that at most 4 calls will arrive in a twenty-minute period?
4.3. What is the probability that more than 2 calls but no more than 5 calls being received in a fifteen-minute period?
4.4. Is Poisson distribution a good model in this case? Explain.
Problem 5. The joint probability distribution of the size of company X's sales force and company Y's yearly sales revenue is represented in the following table:
|
Probability (pi )
|
# of sales people (xi)
|
Yearly sales revenues (yi)
|
|
0.10
|
45
|
4.17
|
|
0.20
|
37
|
3.85
|
|
0.25
|
32
|
2.61
|
|
0.25
|
28
|
1.53
|
|
0.20
|
26
|
1.06
|
5.1. Compute the correlation of the size of the sales force and yearly sales revenue.
5.2. What does the correlation coefficient tell you about the relationship between the size of company X's sales force and company Y's yearly sales revenue?