Question 1:
The monthly average sales of the Smiling Ninja Computer Company may be approximated to a normal distribution curve. It has a mean of $22,000 and a standard deviation of $3,300.
Drawing a curve for each question, calculate the proportions of the following:
a. The proportion of sales greater than $21,500 per month;
b. The proportion of sales less than $21,000 per month;
c. The proportion of sales between $22,500 and $24,500.
Note: Show all relevant workings and draw a normal distribution graph for each part.
Question 2:
a. What is a "Chi-Squared Test"? Provide a fully referenced explanation.
b. Provide a brief example on a Chi-squared test, fully referencing all sources of information.
Question 3:
Part A: You have been offered the choice of 3 prizes;
Prize 1: $15,000 cash payable immediately;
Prize 2: 2 yearly payments of $8,000, with the first instalment due in 1 year's time (assume yearly compounding);
Prize 3: $490 per month for 2 years, with the first instalment due in 1 month's time (assume monthly compounding)
Other information:
Current interest rates are 9% per year.
(a) Based on present values, which prize would you prefer and why? Show workings for all prizes, and explanations in your answer.
(b) What do finance experts mean when discussing "the power of compounding"? Provide a brief example to support your answer.
Part B:
A TV is for sale at $6000. You cannot afford to pay cash, and were offered the following payment methods:
i. Pay 15% deposit upfront and pay the balance over 2 years, in equal monthly instalments. Assuming a simple rate of interest at 12% per year, how much would you pay per month?
ii. What will be the total amount paid?
iii. If you paid cash at the beginning, how much would you have saved?