Question 1
You are a data analyst working for the Australian Petrol Pricing Commissioner and have been requested to provide a comprehensive statistical summary of the NSW fuel price data (FUEL_2011nsw). Furthermore, you are to compare petrol and diesel prices. How you do this is up to you, however you should include relevant tables, graphs, and numerical summary measures presented in a professional style. You should also summarise your findings on the fuel prices in two or three sentences.
Question 2
The Melbourne Cup, held on the first Tuesday in November, has 24 horses entered in it.
a. What is the probability of winning a prize in an office sweep (where horses are randomly allocated), if prizes are given for first, second and third places?
b. In a trifecta three horses are selected to finish first, second and third in the correct order. How many possible trifectas are there in the Melbourne Cup?
c. How many combinations of the horses winning a place (first, second or third) are not trifectas? That is, the selected horses finish first, second and third but not in the correct order.
d. Suppose you have a sweep ticket (where horses are randomly allocated) for the trifecta. What is your probability of winning the major prize (the trifecta) or a consolation prize (having three winning horses but in the wrong order)?
Question 3
In a certain weekday television show, the winning contestant has to choose randomly from 20 boxes, one of which contains a major prize of $100,000.
a. What is the probability that, during a week (i.e., Monday to Friday - five shows per week),
i. No contestants win the major prize?
ii. Exactly one contestant wins the major prize?
iii. No more than two contestants win the major prize?
iv. At least three contestants win the major prize?
b. Calculate the expected number and standard deviation of the winners in a week.
c. How much should the producers budget for major prizes per week?
Question 4
The State fire service has recently set up a specialist rescue unit to respond to road traffic accidents in the area surrounding a small country town. The rescue unit has been in operation for 60 weeks and has been called out 120 times to attend road traffic accidents. The weekly pattern of call out has a Poisson distribution. Find the:
a. Mean demand per week
b. Probability that the rescue unit will be called out in aweek
c. Probability that the rescue unit is called out at least twice in a week
d. Probability that the rescue unit is called out at least once in a two week period.
Question 5
The weight of potato chip packets is normally distributed with a mean of 510g and a standard deviation of 20g.
a. Find the probability that a packet of chips will be below the labelled weight of 500g.
b. A packet can only contain 550g otherwise it will overflow. Find the probability of a packet overflowing.
c. The lightest 5% of packets are rejected at quality control. At what weight does this occur?
d. What is the minimum weight of a packet that is in the heaviest 5%?