Advanced level 2025 Adamawa regional mock pure maths statistics 3
Advanced level 2025 Adamawa regional mock pure maths statistics 3
The examination marks of some pupils in a certain class are given in the table below
Marks, x 5 _ 9 1 0 – 14 15 – 19 20 – 24 25 – 29 30– 34 35 – 39 40 – 44 45 – 49 50– 5 4
Frequency, / 3 4 5 15 22 19 14 10 6 2
(a) Calculate the mean and variance of the distribution of the marks
(b) Draw an orgive of the distribution of the marks
(c) Estimate the median mark and the quartile deviation of the distribution of marks
(6, 2, 5) marks
2. (i) Given that P(A) = 0.4, P(B) = 0.6 and P(A n B ) = 0.2, find P(B) if
(a) A and B are mutually exclusive,
(b) A and B are independent.
(ii) On a given day, a petrol station serves 3 times as many males as female
customers. Two types of fuel, super (S) and diesel (D) are available. 60% of the males and
40% of the females buy super. Customers pay for their fuel either in cash or cheque. Of
the males who buy super, 80% pay in cash while 2 0% of the males who buy diesel, pay in
cash. Of the females who buy super, 60% pay in cash while of the females who buy diesel,
40% pay in cash. Using a tree diagram, find the probability that
(c) A customer buys super,
(d) A customer pays in cash,
(e) A customer who pays in cash for super is a male.
(3, 3) marks
(3, 3, 2) marks
3. The probability mass function of a discrete random variable X is defined by
«*>–P“\
(a) Obtain the value of the constant k
(b) Write down the probability distribution of X
(c) Find E( X ) and Var( X )
(d) Calculate the values of E( UX – 4) and KarCllX – 4)
for x = 0,1,2,3,
otherwise
(3, 3, 6, 4) marks
4. (i) State the principal features of the Poisson distribution.
A manufacturer of components finds that on the average, 2%of the components are
defective. Components are packed in cartons of 50. Use the Poisson distribution to find
the probability that a carton selected at random, will contain
(a) At most 1defective component,
(b) Exactly 2 defective components,
(c) More than two defective components.
(ii) A random variable X has a normal distribution with mean n = 20 and standard
deviation a = 4. Find the probability that an observation X selected at random
(d) Is less thanl5,
(e) Is greater than 25,
| (f) Lies between 18 and 22. | (2, 3, 3) marks |
| A continuous random variable X has probability density function f given by | 5. |
(1, 3, 2, 3) marks
