EC7091 Quantitative Methods for Business and Finance

Statistics Seminar 1 –

Probability and probability distributions

1. Three stocks were monitored for 5 days and their daily prices are recorded below.

Stock A: 2, 3, 2, 3, 5

Stock B: 4, 5, 4.9, 5, 6.1

Stock C: 5, 4.6, 5, 5.4, 5

Calculate the means, standard deviations and the coefficients of variation and compare the stocks on this basis.

2. There are 7 investment portfolio analysts employed by a company and they work in teams of 4. How many ways are there of choosing a team?

3. A consultancy firm employs 7 accountants and 5 lawyers. In a team working on a case there should be 3 accountants and 2 lawyers. How many ways are there of choosing a team?

4. In a particular university 30% of student activists are prepared to serve on an Entertainment Committee, 25% on a Welfare Committee and 10% on both. What is the probability that a randomly chosen student activist will be prepared to serve either on an Entertainment or a Welfare Committee?

5. In order to get an overall Merit Lee needs one more Merit in the two modules still to take. The probability that Lee gets a Merit in Quantitative Methods is 0.7 and the probability that he gets a Merit in Dissertation is 0.9. What is the probability that he will pass his Masters with a Merit?

6. The following table summarises the information about the risk assessment of 15 aerospace companies and 25 food retailers:

Low risk

High risk

Aerospace company

6

9

Food retailer

15

10

One of the total of 40 companies is selected at random.

What is the probability that the company is a food retailer?

What is the probability that the company is rated as high risk?

What is the probability that the company is rated as high risk given that it is an aerospace company?

Is the company type related to the level of risk? Explain.

7. The results of the survey indicated that 8% of customers were not satisfied with...