cameroon gce A level June 2023 pure maths with statistics 3

cameroon gce A level June 2023 pure maths with statistics 3

cameroon gce A level June 2023 pure maths with statistics 3

(i) Two events A and B are such that P( A) = j, P( A U B ) = and P( A n B ) — —.
Find
, (
a) P(fl),
(b) P( A/ B ),
(c) P( B n A’ ). (3, 2, 3 marks)
(ii) A manufacturer of phones employs an inspector to check the qualities of his product. After testing a
large sample from a consignment, the inspector finds out that 2 out of every 10 phones are defective.
A customer buys two of the phones.
Calculate, the probability that
(d) both phones are defective
(e) exactly one phone is defective. (2, 3 marks)
2. The yields, to the nearest kilograms of 150 fruit trees, are given in the table below
Yield, x kg 1 0 – 1 4 1 5 – 1 9 2 0 – 2 4 2 5 – 2 9 3 0 – 3 4 3 5 – 3 9 4 0 – 4 4 4 5 – 4 9
Number of trees, f 4 9 18 2 8 3 9 3 0 1 5 7
Estimate, to two decimal places,
(a) the mean yield,
(b) the standard deviation of the yields.
(c) Draw a cumulative frequency curve for the data.
Using the cumulative frequency curve, estimate
(d) the median yield
(e) the quartile deviation of the distribution. (3, 3, 2, 2, 3 marks)
3. (i) A certain vaccine is administered to a group of persons. It is observed that 0.1% of all the persons who
take the vaccine suffered from a side effect.
Using the Poisson distribution, find, to four decimal places, the probability that out of 1000 persons who
take the vaccine,
(a) none will suffer from the side effect.
(b) exactly two persons will suffer from the side effect.
(c) more than two persons will suffer from the side effect. (3, 2, 3 marks)
(ii) Out of 1000 customers that visit a telephone booth, 60 buy credit cards.
Given that the number of customers buying credit follows a binomial distribution, find, the probability that
in a randomly selected sample of 10 customers,
(d) exactly three buy credit cards
(e) more than seven buy credit cards (2, 3 marks