### A level south west regional mock gce 2022 mathematics with statistics 3

A level south west regional mock gce 2022 mathematics with statistics 3

1. The times taken by a group of students to complete a test are shown in the table below.

Time, in minutes 15 – 19 20 – 24 25 – 29 30 -34 35 – 39

Number of students 2 5 12 8 3

Calculate, giving the answers in two decimal places,

(a) the mean

(b) the standard deviation of the time used by the students to complete the test 8 marks

The following day, the same test was administered to an independent group-of 20 students in another school. The

mean and standard deviation of the time taken by this second group of students to complete the test were obtained

as 28.20 minutes and 6.00 minutes respectively.

Obtain, giving the answers in two decimal places,

(c) the mean .

(d) the standard deviation of the time taken by the two groups of students to complete the test 5 marks

2. (i) Two events Aand B are such that P(_A) l 3 11-

(a) Show that A and B are independent.

(b) Calculate the values of P{A/ B ) and P(B/ A)

3’ P( B) = – and P( A U B ) = 15

6 marks

(ii) A trader receives merchandise from two suppliers, Andrew and Bernard, with 60% being supplied by

H Andrew. It has been observed that 30% of the merchandise supplied by Andrew and 20% of the

merchandise supplied by Bernard are always of doubtful quality.

(c) Draw a tree diagram to illustrate this information. ,

(d) The trader places an order for 10000 pieces of merchandise. Estimate the number of pieces that are

> expected to be of doubtful quality.

(e) Find the probability that a doubtful quality piece received was supplied by Bernard 7 marks

3. The probability density function of a continuous random variable X, f(x) , is defined by

Find the value of the constant k.

f Calculate the mean and variance of 2f. ^ :

Show that the 80th percentile of X,e ,satisfies the equation 5e3 — 15e2 + 16 = 0

4. (i) A random variable X has a probability mass function defined by

f c( x +1) , x = 0 ,1, 2 ,3,

(3, 7,3) marks

f(x) =

0 , otherwise.

(а) Determine the value of the constant c.

(б) Find the mean and variance of X .

(ii) In the first trial of an experiment, the probability of success is

In the second trial, the probability of success will be- if the first trial was successful, but it will be- if the

first trial was not successful.

If Y is defined as “the number of successes”, show that Y is a random variable