Business Statistics Spring 1997

BUSINESS STATISTICS SPRING 2003

Tutorial 4

Week beginning: 25 August 2003 Due date: 7 October 2003 Value: Tutorials 4 - 6 consolidate the unit of work on Probability and Probability distributions. These three tutorials combined represent 10% of the overall assessment. Marking criteria: Marks will be awarded for:  the correct answers;  appropriate detailed working;  clear and valid explanations where appropriate.

In this tutorial you will consolidate the work done in lectures on probability. Work can be handwritten as long as it is neatly and tidily presented with the usual cover sheet.

1. Suppose that P(A)  0.60, P(B)  0.45 and P(A and B)  0.30. a. Find P(A or B), P(A | B) and P(B | A). b. Are the events A and B mutually exclusive? Why or why not? c. Are the events A and B independent? Why or why not?

2. A marketing firm was looking at the type of medication that people with allergies took during the spring allergy season. In particular, the firm wanted to know whether the person took medication daily and whether that medication was prescribed by a doctor or purchased over the counter.

Prescription Over the counter Totals Took medication daily 83 40 123 Took medication as needed 21 156 177 Totals 104 196 300

a. What is the probability that an allergy sufferer was prescribed medication by a doctor? b. What is the probability that an allergy sufferer took medication daily? c. What is the probability that an allergy sufferer had a prescription medication and he/she took this daily? d. What is the probability that an allergy sufferer was prescribed medication by a doctor, given that they take medication daily? e. Is whether an allergy sufferer takes medication daily independent of whether they were prescribed the medication by a doctor? Use probability values to explain.

3. An insurance company classifies drivers as low-risk, medium-risk and high-risk. Of those insured, 60% are low-risk, 30% are medium risk and 10% are high risk. After a study, the company finds that during a one-year period, 1% of the low-risk drivers had an accident, 5% of the medium risk drivers had an accident, and 9% of the high-risk drivers had an accident.

a. If a driver is selected at random, find the probability that the driver will have had an accident during the year. b. An insured driver has had an accident and has made a claim. What is the probability that they are a high-risk driver?

Work to be completed and handed in by 5pm, 7 October 2003, in the assignment box in Building 1. Questions may be neatly handwritten showing appropriate working. Each tutorial must have a cover sheet showing your name, student number, tutorial day and time, and tutorial number ie Tutorial 4. All three tutorials should be bundled together unless you choose to submit each separately, as completed.