Critically assess the view that an understanding of the principles of

'scientific' decision-making is fundamental to the success of a modern

economy.

Examination questions and answer notes 335

2. (i) Explain the concept of opportunity loss, and show that the

minimum opportunity loss is equal to the Expected Value of

Perfect Information.

(ii) The failure rate in a particular examination is estimated to be

40%. Construct a table showing the probabilities of 0, 1, 2 . . . 5

students failing in a sample of five.

(iii) 150 graduate entrants are due to take their first professional

accounting exam at the Institute of Certifiable Accountants.

The probability distribution for the failure rate is estimated in

the following table:

Failure rate

0.1

0.2

0.3

0.4

0.5

Probability

0.1

0.2

0.3

0.3

0.1

Each failing student is entitled to a 10 refund on professional

fees. The Institute's senior tutor is confident that she could

ensure a failure rate of 0.1 by holding an intensive revision

course, at a cost to the Institute of 300. Advise the Institute on

whether the revision course should take place.

A tutorial test of five students resulted in no failures. Use this

information to revise the failure rate probability distribution,

and hence reassess the revision course.

3. 'Despite being a small local shopkeeper I can always beat the price

that Woolworths charge for the same product. Woolworths must pay

rent on its store while I own my shop and have no rent to pay.'

Discuss.

4. A firm keeps a record of sales and prices over the past seven months,

resulting in the following table:

Nov. 1985

Dec.

Jan. 1986

Feb.

March

April

May

Price (/ton)

7.5

8.0

8.0

7.2

7.0

8.0

8.5

Sales (tons)

84.5

82.0

84.0

92.0

95.0

92.0

91.5

Use these observations to estimate demand as a linear function of

both price and time. Utilize this function to estimate demand for the

following month, on the assumption that:

(a) price remains unchanged,

(b) price increases to 9/ton.

7. (14 marks). Dr. Poincaire teaches both calculus and introductory differential equations, often to the same (a) (I!) (C) (d) (at students. Passing the calculus course was a prerequisite to taking the differential equations course. Dr. Puincaire was curious as to whether the calculus grade could be used to predict the differential equations grade in some way. He randomly selected 12 former students who had taken both courses from him and created the following table (grades for both course are out of 100). Student I 2 3 4 5 6 7 8 9 ID 1 l 12 Grade in calculus 1' 81 63 T5 33 70 55 67 T4 74 96 89 70 Grade in differential equations 3: 91 75 92 39 75 65 32 TD 72 95 90 61 The following summary shows the sums required to perform linear regression analysis. 293,. = 397 2 y,- = 957 23:: = 68447 Z 3;? = 77795 Zrtyi = 72510 (5 marks). Show explicitly the calculations to nd E, E, S\Solve the following differential equation. 11. f"(0) = 2 - sin (0) where f(0) = 1 and f =-1Question 1. (a) Could the separation of variables technique be used to solve the following differential equations? Give a single-sentence explanation in each case. (i) dy = dt (ii) dy zy+1 dt (iii) dy - tty dt (iv) dy - ty ty dt (b) Solve the initial value problem dy y(0) = 3. dt = 2t(y - 5),B - S2:OM4AB - AP Calculus AB - S2 / HW-8.2 ew Exercises, Question 003 ation by the method of separation of variables. dy = 2 (1 + 1 2) x2 2 4 4 dx the arbitrary constant in the general solution appears * (keeping the coefficient on the right-hand side) a