Advanced level 2023 south west regional mock pure mathematics with statistics 3

Advanced level 2023 south west regional mock pure mathematics with statistics 3

Advanced level 2023 south west regional mock pure mathematics with statistics 3

l(i) TwoeventsAandBare such thatP(A)=p P(B{A) — -, P(B/A ) —.Find,
(a) P(/infl)
(b) P( B )
(c) P(A/B’ )
(ii) The papers of an engineering exam are Mathematics, Physics and Chemistry. The probabilities
that John will succeed in these papers are |and -, respectively. If he passes In all the
papers, he will succeed in the exam. If he fails in just one paper, his name will be on the waiting
list. Find the probability that
(a) he succeeds in the exam,
(b) his name is on the waiting list.

2 The marks
, out of 50, scored by 100 students in a mathematics examination are summarized
in the table below ‘
Marks (x) 10 – 14 15 – 19 20 -24 25 -29 30 – 34 35 – 39 40- 44
No. of 20 14 7
students
4 9 21 25
in
(7 marks)
(2 marks)
{a) Calculate, to 2 decimal places, the mean and standard deviation of the marks.
(b) Draw a cumulative frequency curve for this distribution.
(c) To obtain an “A” grade, a student must score at least 36. Using the curve, determine the
percentage of students who scored an A grade. (4 marks)
3 A discrete random variable X has the following distribution:
(a) Find the value of f,
Given that /T(A’)- 4.5, find,