General guidelines:
a) The assignment must be produced in Microsoft Word and a printed copy requires to be submitted by the due date.
b) You might use Microsoft Excel or any statistical software. Please set in or copy and paste any relevant outputs into the Microsoft Word document.
c) Answer all five problems and clearly illustrate your workings (that is, how you developed your answer). If your tutor or lecturer can’t readily comprehend your calculation steps and assumptions, they might be unable to award you full marks for your answers.
d) This is an individual assignment. Students who are found to have copied other student’s work or shared their work with other students will be subject to profound penalties. (Note: Please see the STA1000 Subject Outline for a explanation of the Kaplan Business School requirements for academic integrity).
problem:
You are a data analyst working for the Australian Petrol Pricing Commissioner and have been requested to give a comprehensive statistical summary of the NSW fuel price data (FUEL_2011nsw). In addition, you are to compare petrol and diesel prices. How you do this is up to you, however you must comprise relevant tables, graphs and numerical summary measures presented in a professional style. You should as well summarize your findings on the fuel prices in two or three sentences.
problem:
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 provided for first, second and third places?
b) In a trifecta three horses are chosen 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 chosen horses finish first, second and third but not in the accurate order.
d) Assume 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 (containing three winning horses but in the wrong order)?
problem:
In a certain weekday television show, the winning contestant has to select 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),
• No contestants win the major prize?
• Exactly one contestant wins the major prize?
• No more than two contestants win the major prize?
• At least three contestants win the major prize?
b) Compute the expected number and standard deviation of the winners in a week.
c) How much should the producers budget for major prizes per week?
problem:
The State fire service has lately set up a specialist rescue unit to respond to road traffic accidents in the region 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. Determine the:
a) Mean demand per week.
b) Probability which the rescue unit will be called out in a week.
c) Probability which the rescue unit is called out at least twice in a week.
d) Probability which the rescue unit is called out at least once in a two week period.
problem:
The weight of potato chip packets is normally distributed with a mean of 510 g and a standard deviation of 20g.
a) Find out the probability that a packet of chips will be below the labeled weight of 500g.
b) The packet can only contain 550g or else it will overflow. Find out the probability of a packet overflowing.
c) The lightest 5% of packets are refused at quality control. At what weight does this take place?
d) What is the minimum weight of a packet that is in the heaviest 5 percent?