Mathematics T

Name : ………………………………………………… Class : ………..…….…..
I.C Number : ……………………………........…………

KOLEJ TINGKATAN ENAM SHAH ALAM
JALAN TIMUN 24/1

SHAH ALAM SELANGOR DARUL EHSAN

PEPERIKSAAN PERTENGAHAN SEMESTER 3 STPM 2021

MATHEMATICS T
954/3

PAPER 3
DURATION : 1 Hour 30 Minutes

DO NOT OPEN THIS BOOKLET UNTIL YOU ARE
ALLOWED TO DO SO

This question paper consists of 3 printed pages

1

Section A [45 marks]

Answer all questions

1. The table below shows the numbers of cars sold by 70 agents of a car company
during a period of one week.

Numbers of cars 1 - 5 6 - 10 11 - 15 16 - 20 21 - 25 26 - 30 31 - 35
Numbers of agents 2 9 14 20 16 8 1

Plot a cumulative frequency curve for the data [3 marks]

Hence, estimate the percentage of agents who sold less than 19 cars in a week [2 marks]

2. A label on a sudden packet drink reads “net content 250 ml “. The contents (xml) of 100 packets
are measured and are summarised by

∑ ( x - 250) = 180 , ∑( x - 250 ) 2 = 1348

Find the mean and standard deviation of the contents of the packet drinks. [5 marks]

3. a. In how many ways can 2 boys and 5 girls be arranged in a row if the two boys are not

together? [4 marks]

b. A family consists of a father, a mother and seven children. They are required to send a

group of five representatives to a function. Find the number of ways in which the group

can be formed it it must consist of

i. both father and mother

ii. neither parents

iii. only one of the parents [6 marks]

4. a. It is given that 60% of the workers in a factory are female. 20% of the female workers and

50% of the male workers drive to work everyday. A worker is selected at random.

Find the probability that the worker

i. drives to work everyday [2 marks]

ii. is a male given that the worker drives to work everyday [2 marks]

If two workers are selected at random, find the probability that none of them drives

to work everyday [2 marks]

b. If A and B are events and P(B) = 1 , P(A∩B) = 1 , P(B/A) = 1 ,calculate P(A),
6 12 3

P(A/B’ ) where B’ is the event B does not occur. State, with reason, if A and B are

i. independent of each other

ii. mutually exclusive [4 marks]

5. a. The expected number of pupils who fail the Economics test is 2.4 and the variance is 1.92 .

Find the probability that exactly 3 pupils fail the test. [5 marks]

b. If X and Y are Poisson variables with mean 1 and 1.5 respectively, find

P(X + Y = 2) [4 marks]

6. The marks of a test are distributed normally with mean 55 and standard deviation 12.

2

Pupils who obtained 75 marks or more are given grade A, and pupils who obtained 85 marks or

more are given certificate of excellence.

a. Find the probability that a pupil gets a grade A [3 marks]

b. Find the probability that a pupil who gets a grade A will also be given a certificate of

excellence [3 marks]

Section B [15 marks]
Answer one question only
You may answer all the questions but, only the first answer will be marked.

7. The masses (in thousands of kg) of solid waste collected from a town for 25 consecutive days
are as follows:

41 53 44 55 48 57 50 38 53 50 43 56 51
48 33 46 55 49 50 52 37 39 51 49 52

a. Construct a stemplot to represent the data [2 marks]
b. Find the median and interquartile range [4 marks]
c. Calculate the mean and the standard deviation [4 marks]
d. Draw a boxplot to represent the data [3 marks]
e. Comment on the shape of the distribution and give a reason for your
[2 marks]
answer

8. a. A random variable X has the probability distribution given in the following table

x 23 4 5

P(X = x) p 3 2q

10 10

i. Given that E(X) = 3.9 , find p and q [5 marks]

ii. Find Var (X) [3 marks]

iii Find E(| − 3|) [2 marks]

b. The continuous random variable X has cumulative distribution function given by

F(x) = 0 for x < 0. 5
2 − 1 for 0.5 ≤ < 1

1 for x ≥ 1

i. Find the median of X [2 marks]
[3 marks}
ii. Find P ( X ≥ 3 )
4

3