### cameroon gce A level 2024 business mathematics 3

cameroon gce A level 2024 business mathematics 3

Three events A, B and C are such that P( A) = 1 / 3 />(0 = 5 / 7 and P(AUB)- 1 /2.

Find:

(a)-P(B),if A and B are mutually exclusive

(b) P(B),if A and B are independent.

(c) P(AflC),if A and C are exhaustive

(d) Two cards are drawn at random one at a time without replacement from a pack ot 52 cards, f ind the probability

{4 marks)

(5 marks)

* $ (5 marks)

that:

•

* » A (2 marks)

(4 marks)

Total = (20 marks)

The two cards drawn are picture cards

The two cards are of the same suit

(a) Define the following under network analysis

i. activity

events

in. critical path

iv. dummy activities

(1.5 x 4 = 6 marks)

(b) The following table gives data for a simple project i •

Activity Preceding activity Duration(days)

i. Draw up a network

ii Identify the critical path and its duration

(12 marks)

(2 marks)

Total = (20 marks)

4. The revenue gotten from the sales of \ 50 pencils is given below:

‘

Profit in FCFA * 1 0 – 1 4 15 – 19 2 0 – 2 4 2 5 – 2 9 3 0 – 3 4 3 5 3 9 4 0 – 4 4 4 5 – 4 9

No of pencils 4 9 18 28 39 30 15 7

(a)Estimate to one decimal place the mean and the Standard Deviation

(a) Construct the cumulative frequency curve

(b) From the cumulative frequency curve, estimate the semi-interquartile range

Total = (20 marks)

In its quality control procedures, a firm sets the warning limit at the 0.025 probability point and the action limit at

the 0.001 probability point. This means for example that the upper action line is set so that the probability that the

mean exceeds this line is 0.001. The length of a product is normally distributed with a mean length of 100 cm and a

known standard deviation of 0.4 cm. to check on the process, samples of 6 products are taken from the production

line.

(a) Draw a control chart to monitor the production process

(b) The first ten samples had the following mean length in cm.

100.3 ; 99.8 ; 99.9 ; 100.4 ; 100.2 ; 99.7 ; 99.6 ; 99.7 ; 99.6 ; 99.4

Plot these values on your control chart and comment on the result