There are total of 4 sections:- Section 1 – basic probability theory (2 questions) Section 2- Discrete probability distribution (3 questions) Section 3- Continous Probability theory (1 question) Section 4- Sampling distribution (1 question)
Faculty of Business, Economics and Law
Bachelor of Business
Trimester 1 2020
Section 1 – Basic Probability Theory
Question 1 (9 Marks)
A disease has a 5% prevalence in the population. You need to choose between two tests.
Question 2 (9 Marks)
Poker is a game played with a standard deck of 52 cards. The aim of a hand of poker is to finish with the strongest five card combination. In straight draw poker, each player is dealt five cards. Players are then given a single opportunity to discard as many cards as they wish and have them replaced with new cards off the top of the deck. In the questions that follow, only your hand is being dealt from the deck of cards (i.e. you do not need to worry about cards dealt to other players).
On the initial deal:
What to keep:
Section 2 – Discrete Probability Distributions
Question 3 (7 Marks)
You wish to form an investment portfolio, and have three assets to choose from, a high-risk asset A, and medium-risk asset B, and a zero-risk asset C.
The returns per $1,000 invested for each of these assets in each of three possible economic conditions is give in the table below:
|Asset A||Asset B||Asset C|
Question 4 (5 Marks)
A cloth manufacturer measures defects per metre of cloth, and estimates that on average, there is one flaw per five metres of cloth. What is the probability that:
Question 5 (5 Marks)
A government tax office auditor is to select and audit six tax returns from a batch of 100. If two or more of the selected returns contain errors, the whole batch will be audited.
Section 3 – Continuous Probability Distributions
Question 6 (5 Marks)
A trucking company was worked out that on average its trucks drive 100,000 kilometres a year, with a standard deviation of 20,000 kilometres. The distances driven are normally distributed.
Section 4 – Sampling Distributions
Question7 (5 Marks)
In the first quarter of 2014, the rental cost of a three-bedroom house in a regional town was $300 with a standard deviation of $30. Assume that the rental costs are normally distributed. If you select a random sample of ten rental properties, what is the probability that the sample will have a mean rental cost of:
 If you are not familiar with playing cards, see here: https://en.wikipedia.org/wiki/Standard_52-card_deck . If you are not familiar with poker, see here: https://en.wikipedia.org/wiki/Poker . You need to know the composition of a deck, but the questions should not require knowledge of the game.
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