Advanced level 2026 south west regional mock mathematics with statistics 3

Statistics & Probability Mock Exam – Paper 3 (Section Extract)

(1) The marks of 80 students in Literature in English of a certain school of form four are summarized as shown on the table below.

Calculate the:

(a) Mean mark of the students

(b) Standard deviation of the students marks

(c) Draw a cumulative curve for the marks.

(d) Hence or otherwise estimate the median marks.

(4, 4, 3, 2) marks

(2) (i) Two independent events A and B are such they $P(A) = \frac{3}{10}$ and $P(B) = \frac{2}{5}$.

Find:

(a) $P(A \cap B)$

(b) $P(A \cup B)$

(c) The probability that neither A nor B occurs

(2, 3, 3) marks.

(ii) A box contains 2 red, 3 blue and 4 yellow marbles. Two of these marbles are drawn from the box without replacement.

(d) Draw a tree diagram showing all its possibilities.

(e) Hence or otherwise find the probability that a red and yellow marble is drawn.

(3, 2) marks.

(3) A discrete random variable, $X$, with probability density function defined

Calculate:

(a) The constant $C$

(b) The mean of $X$

(c) The variance of $X$

Another random variable, $Y$, is defined by $Y = 3X – 1$

(d) Calculate the mean and variance of $Y$

(3, 3, 4, 3) marks.

(4) The continuous random variable, $X$, has probability density function, $f$, given by

Given that $E(X) = \frac{3}{5}$

Calculate:

(a) The values of the constants $a$ and $b$

(b) The variance of $X$

(c) Show that the lower quartile, $l$, satisfies the equation $2l^4 – 6l^2 + 1 = 0$

(5, 4, 4) marks.

Source Information:

© TRU/RPI-Sc/SWAMT/PMS/0770/P3/MOCK 2026 | pg. 2/3