The Association of Business Executives Certificate

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4. 
   (i)Those costs that remain constant irrespective of quantity produced (i.e. fixed costs) have increased.
   

Those costs that vary with quantity produced (i.e. variable costs) have decreased.

(ii)

C=R

2500 + 30x = 200x – 2.5x ^2

2.5x ^2 – 170x + 2500 = 0

170 ±

170^2 –

(

4 × 2.5

× 2,500

)

x =

170 ±

28,900 – 25,000

x =

2 × 2.5

5

x =

170 ±

3,900

x =

170 ± 62.45

x = 21.5 or 46.5

5

5

Q8 (a) (i)

Variables may be either continuous or discrete. A continuous variable may take

any value between two stated limits (which may possibly be minus and plus

infinity). Height, for example, is a continuous variable, because a person’s height

may (with appropriately accurate equipment) be measured to any minute fraction

of a millimetre.

A discrete variable, however, can take only certain values occurring at intervals between stated limits. For most (but not all) discrete variables, these interval values are the set of integers (whole numbers).

For example, if the variable is the number of children per family, then the only possible values are 0, 1, 2, etc. because it is impossible to have other than a whole number of children. However, in Britain, shoe sizes are stated in half-units, and so here we have an example of a discrete variable which can take the values 1, 1½, 2, 2½, etc.

35. 
    In its strictest sense, primary data is data which is both original and has been obtained in order to solve the specific problem in hand. Primary data is, therefore, raw data and has to be classified and processed using appropriate statistical methods in order to reach a solution to the problem.
    

Secondary data is any data other than primary data. Thus, it includes any data which has been subject to the processes of classification or tabulation or which has resulted from the application of statistical methods to primary data, and all published statistics.

2. 
   (i)If two events are mutually exclusive then the occurrence of one event precludes the possibility of the other occurring. For example, the two sides of a coin are mutually exclusive since, on the throw of the coin, “heads” automatically rules out the possibility of “tails”. On the throw of a die, a six excludes all other possibilities. In fact, all the sides of a die are mutually exclusive; the occurrence of any one of them as the top face automatically excludes any of the others.
   

35. 
    Non-mutually-exclusive events are events which can occur together. For example, in a pack of playing cards hearts and queens are non-mutually-exclusive since there is one card, the queen of hearts, which is both a heart and a queen and so satisfies both criteria for success.
    

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3. 
   Independent events are events which are not mutually exclusive and where the occurrence of one event does not affect the occurrence of the other. For example, the tossing of a coin in no way affects the result of the next toss of the coin; each toss has an independent outcome.
   

3. 
   Dependent or non-independent events are situations where the outcome of one event is dependent on another event. For example, the probability of a car owner being able to drive to work in his car is dependent on him being able to start the car. The probability of him being able to drive to work given that the car starts is a conditional probability.
   

3. 
   An event either occurs or it does not occur, i.e. we are certain that one or other of these situations holds. For example, if we throw a die and denote the event
   

where a six is uppermost by A, and the event where either a one, two, three, four
— —
or five is uppermost by A (or not A), then A and A are complementary, i.e. they are mutually exclusive with a total probability of 1.

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