cameroon gce advanced level June 2022 pure maths with statistics 3

cameroon gce advanced level June 2022 pure maths with statistics 3

cameroon gce advanced level June 2022 pure maths with statistics 3

(i) Two events A and B arc such that P(/l) =^,P(B) =^ and P(Au C) =^.
rind
(a) P(A n B),
(b) P(A’ n B),
(c) P(B/ A). (3, 2,2 marks)
(ii) A bag contains 3 red balls and 5 blue balls. One ball is selected at random from the bag and replaced by a
ball of the other colour. A second ball is selected.
Find the probability that
(d) both balls arc of the same colour. *
(e) the first ball is red given that the second ball is blue. (3,3 marks)
2. The weekly wages,in thousands, of a group of 80 part time workers in a certain bakery is as shown in the
frequency distribution below.
Wagcs(in thousands) I – 10 11-20 21-30 31-40 41-50 51-60 61-70
Number of workers 5 15 22 18 10 8
(a) Calculate the mean and standard deviation of the wages.
(b) Draw a cumulative frequency curve for this distribution.
Using the cumulative frequency curve, estimate,
(c) the median wage,
(d) the number of workers who earn more than 55000 per week. (7, 2,2,2 marks)
3.(i) The number of telephone calls made to an emergency unit in a hospital per hour follows a Poisson distribution
with mean 2.5.
Find, to 4 decimal places, the probability that
(a) just one call is made in a period of one hour.
(b) at least one call is made in a period of one hour.
(c) no call is made in a period of two hours.
(ii) A discrete random variable X is such that X ~ D(d,
Find
(a) l\X = 2)
(b)
P( X 1)
(2,3,3 murks)
(2,3 murks)
4. A continuous random variable X has probability density function, f, where
f(x) = 0 * 3
0 elsewhere.
Find (a) the value of the constant k,
(b) the mean and variance of X.
Show that the upper quartile,u, of the distribution satisfies the equation 8tta – 36u2 + 81 = o