2.2 A manager informs 2 employees, Annie and Caroline, that their performance will

be rated according to categories with the percentage weightings shown in the

Table below. The one who obtains the largest weighted mean score will be

awarded a salary rise.

Category Weighting

Initiative 30%

Creativity 50%

Ability to meet deadlines 20%

Annie and Caroline are given score out of 10 in each category, and their scores

are shown below.

Category Annie's scores Caroline's scores

Initiative 3.5 6.0

Creativity 8.0 6.5

Ability to meet deadlines 5.5 8.0

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2.2.1 Calculate the unweighted mean score for each employee, state who get

salary rise sing this method. (4)

2.2.2 Calculate the weighted mean score for each employee, and state who get

salary rise using this method (6)

.

QUESTION THREE [30]

The age of the population in Wakanda is shown in the following table in the form of a

grouped frequency distribution.

Age (years) Number ('000)

0 Under 5 1 375.3

5 under 15 2 750.5

15 under 30 4 514.7

30 under 50 6 137.7

50 under 65 3 821.7

65 under 80 2 045.7

80 under 100 783.2

100 under 110 3.1

Total 21 431.8

Use the data in the table above to estimate for of population in Wakanda the:

3.1 median age. (4)

3.2 modal age. (3)

3.3 mean age. (3)

3.4 interquartile range. (7)

3.5 coefficient of variation. (8)

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3.6 Construct the downward sloping ogive and indicate on the graph the median

calculated in question 3.1 above. (5)

QUESTION FOUR [20]

4.1 A box contains 5 red balls, 6 white balls and 9 black balls. Two balls are drawn at

random. (The first ball is not replaced). Find the probability that both balls are of

the same colour. (4)

4.2 At the Durban beachfront it rains on 20% of days and it is windy on 30% of days.

If rain and wind are independent, any particular day find the probability that:

4.2.1 it rains and is windy. (3)

4.2.2 it does not rain and is not windy. (3)

4.2.3 it rains or is windy. (3)

4.2.4 it does not rain or is not windy. (3)

4.3 Draw a Venn diagram to illustrate the data in question 4.2 above. (4)