Question 1

A company plans to launch a new product. They have traditionally had a 60% success rate with the launch of new products. Market research predicts that a positive test market results is 80% of successfully launched products and a positive market result for 30% of failed product launches.

a) If a market test result comes back negative, what is the probability that the product will be successfully launched? (5)

QUESTION 2

An insurance company found that 35% of all insurance policies are terminated before their maturity date. Assume that ten polices are randomly selected from the company's policy database. Out of the ten randomly selected policies;

a) What is the probability that at least eight will not be terminated?

b) What is the probability that more than three but less than seven policies will be

terminated?

QUESTION 3

A short term insurance company receives three motor vehicle claims, on average, per day. Assume that the daily claims follow a Poisson process.

a) What is the probability that more than four but less than eight motor vehicle claims will be received on any given day? (5)

b) What is the probability that more than two motor vehicle claim is received over any given period of three working days? (5)

QUESTION 4

The purchase value of transactions at a grocery store is normally distributed with a mean of N$ 244 and a variance of 4624 (N$ squared).

a) What is the maximum purchase value of transactions for the lowest-spending 33% of grocery store customers? (5)

b) What is the probability that the purchase value of transactions of grocery store customers are between N$ 159.00 and N$ 271.20?

QUESTION 5

The following joint probability table shows the information for a sample of 200 companies with one variable indicating the industry and the other variable indicating the sector in which a company is operating:

Sector Retail Formal 0.03 Informal 0.17

Industry

Financial

0.24 0.56

a) If it is known that a company is in the financial industry, what is the probability that it operates in the informal sector? (3)

b) If it is known that a company is not in the financial industry, what is the probability

that it operates in the informal sector? (4)

c) What conclusion can be drawn by comparing the answers in a) and b)

QUESTION 6

A company produces fruit juice in five different flavours (Mango, Guava, Apple, Grape and Tropical). A local supermarket sells the product, but only has sufficient space to display two of the company's five fruit juice flavours at a time.

a) What is the probability that the two flavours displayed are Guava and Grape?