MA1 - C4 - Q1

A company is assessing the expected profitability from a proposed business venture. It has been estimated that there is a 0.5 probability of making a profit of $64,000 and a 25% probability of a loss of $20,000. What is the expected value of the profit from the venture?

• $14,500

• $18,000

• $29,500

• $39,500

The following statements relate to the calculation of a line of best fit for y = a + bx using the formulae in the formula sheet for your examination. (i) n represents the number of pairs of data used (ii) Σx² is calculated as the square of Σx (iii) Σxy is calculated by multiplying Σx and Σy Which of the statement is/are correct?

• (i) only

• (i) and (ii) only

• (ii) and (iii) only

• (i) and (iii) only

Regression analysis is being used to find the line of best fit (y = a + bx) from five pairs of data.

The calculations have produced the following information:

∑x =258, ∑y =2,670, ∑xy =138,546, ∑x² =13,732, ∑y² =269,361

What is the value of ‘a’ in the equation for the line of best fit (to the nearest whole number) calculated from this data?

• 439

• 457

• 629

• 734

Regression analysis is being used to find the line of best fit (y = a + bx) from eleven pairs of data.

The calculations have produced the following information: ∑x =440, ∑y =330, ∑x² =17,986, ∑y² =10,336, ∑xy =13,467 and b = 0.69171

What is the value of ‘a’ in the equation for the line of best fit (to 2 decimal places)

• 0.69

• 5.33

• 2.33

• 0.63

The relationship between national income (X) and demand for a company product (Y) was investigated using regression analysis, based on data from the last 10 years. The value of b calculated was –0.7. Which two of the following statements are consistent with this value of b?

• The product is inferior and, as income rise, people buy higher quality products

• As incomes rise, demand for the product increases

• National income declined over the past 10 years, but sales of the product increased due to heavy advertising

• Demand for the product is determined by the level of national income

An internet service provider charges its customers a fixed connection fee per quarter. Usage is free up to a certain level, after which it is charged at a constant rate per minute up to a higher threshold level, beyond which no further charges are made. Which of the following graphs shows the total cost to the customer of the services in a quarter?

• A

• B

• C

• D

The probabilities used in calculating expected values are estimates. If these estimated probabilities are ...then the expected values will also be unreliable.

​ The characteristics of high low analysis are​ (a)   ​ ​ (b)   ​ ​

​ (c)  

• easy
• simple
• requires extensive data
• complex
• difficulty
• quick
• slow

A decision is a choice between two or more....

An expected value can also be described as the