1. Retail price of fuel in Fiji is uniformly distributed between $2.00 and $3.50 per litre.

a. Calculate the retail average price of fuel in Fiji. (1 mark)

b. What is the probability that the price of fuel will be less than $3. Show working. (2 marks)

c. What is the probability that the price of fuel will less than $2. Show working. (2 marks)

2. List three ways in which we can determine a good model fit? (3 marks)

3. A sample of eight vehicle owners was taken to estimate the demand for vehicle on the weekly price of fuel. The demand for vehicles per month is (X) and the price of fuel per week in $ is (Y).

Obs.

X

Y

X^2

X*Y

Predicted

Y

Residuals

SSE

SSR

SST

1

5

20

2

3

23

3

7

15

4

9

11

5

2

27

6

4

21

7

6

17

8

8

14

Sum

Calculate the x^2, x*y, predicted y, residuals, SSE, SSR and SST? (7 marks)

4. Some high school teachers, teaching schools in outer islands demand an increase in meal allowance. According to a recent survey, the average cost of a meal is $6 in Ba. Suppose this figure is based on a sample of 27 different restaurants with a sample standard deviation of $1. Construct a 95% confidence interval for the population mean cost of a fast food meal in Ba. Assume that the cost of fast food meals in Ba is normally distributed. (5 marks)

5. Let X represents the number of computers in an Australian household, for those that own a computer.

X

1

2

3

4

5

P(x)

.25

.33

.17

.15

.10

a. Find and interpret the expected number of computers in a randomly selected Australian

household. (2 marks)

b. What is the probability that a randomly selected Australian household will have more than 2

computers? (1 mark)

c. Find V (4X +2). (1 mark)

d. Find E(30X + 20]. (1 mark)

6. When is the sample mean normally distributed? (5 marks)

7. Ecologists have a long advocated recycling newspaper as a way of saving trees and reducing landfills. In recent years, a number of companies have gone into the business of collecting used newspapers from households and recycling them. A financial analyst for one such company has recently calculated that the firm would make a profit if the mean weekly newspaper collection from each household exceeded 1 kg. In a study to determine the feasibility of a recycling plant, a random sample of 100 households showed that the mean and the sample standard deviation of the weekly weight of newspapers discarded for recycling are (mean =1.1kg and SD=0.35Kg). Do these data provide sufficient evidence at the 1% significance level to allow the analyst to conclude that a recycling plant would be profitable? [Define your parameter and show all 6 steps procedure] (10 marks)