Semester 3 STPM 2020 Trial Exam Paper

Name: ………………………………… Ting: ……………..

No.kad Pengenalan ;…………………

MATHEMATICS T
PAPER 3
Feb 2021
1 1/2 HOUR

KOLEJ TINGKATAN ENAM SHAH ALAM
JALAN TIMUN 24/1

SHAH ALAM SELANGOR DARUL EHSAN

SEMESTER 3 TRIAL EXAMINATION
STPM 2020

MATHEMATICS T

PAPER 3 (954/3)
TIME : 1 1 HOUR

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Instructions to candidates:
Answer all question in section A and any one question in Section B. Answer may be written in either

English or Bahasa Malaysia.
All necessary working should be shown clearly. Scientific calculator may be used.

Prepared by: Checked by: Validated by:

………………………. ………………………. ……………………….
Che Saidin B. Abdullah
Head of Mathematics T Unit Science and Mathematics Head of

Pn Chin Li Mei Department

Pn.Maziah Muhammad Zin

Kertas soalan ini mengandungi 2 muka surat bercetak

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Section A [45 marks]
Answer all questions in this section

1. Two banks, A and B each chose 25 of their customers randomly. The table below
shows the waiting times ( in minutes) for their customers.

Bank A Bank B

3 18 21 8 12 5 13 19 12 28

19 5 11 25 10 30 15 26 15 16

12 13 10 5 15 15 6 3 21 22

14 9 15 17 24 24 18 17 10 22

22 12 28 32 17 20 24 24 25 20

(a) Construct a back-to-back stem-and-leaf diagram for the data above and [5 marks]
give a comment on the waiting times for both bank. [2 marks]

(b) Comment of the skewness of the two distributions.

2. Events A and B are such that P(A) = 1 , P(A / B) = 3 , and P(A  B) = 7 . Find
2 10 10

P(B), P( A  B) , and P(A'B) . [5 marks]

3. The random variable X has a binomial distribution with parameters n = 500 and

Choose a suitable approximation distribution and justify your answer. [2 marks]
Find P( X − E(X) )  20) [6 marks]

4. A teacher wishes to estimate the number of vehicles that pass by his school.

(a) According to a previous study, the standard deviation of the number of vehicles

passing by his school per day is 245. Calculate the number days required so that he

is 99% confident that the estimate is within 100 vehicles of the true mean. [3 marks]

(b) The standard deviation of the number of vehicles is actually 356. Based on the [3 marks]
sample size in (a), determine the confidence level for the estimate to be within 100
vehicle of the true mean.

5. What is hypothesis testing. [2 marks]
What is mean by null hypothesis in hypothesis testing.

The mean score for a test for entering a teaching college is 65. A random sample of
33 candidates from the current year batch give the following scores :

53 59 79 39 78 79 86 79 42 65 90
75 48 69 71 58 61 73 64 59 41 38
79 71 63 81 84 82 45 83 76 52 73

A lecturer wants to know whether there is statistical evidence for claiming that the
current year’s candidates are above average.

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Carry out a hypothesis test at 5 % significance level, is the claim that the current [7 marks]
year’s candidates are above average is true ?

6. An environmentalist investigates whether there is association between temperature

and air quality. Temperature and air quality of 200 randomly selected days are

recorded as follows :

Air quality

Good Moderate Unhealthy

Low 25 20 11

Temperature Moderate 28 27 16

High 18 21 34

Perform a chi-square test at the 5 % significance level to determine whether there is [10 marks]
an association between temperature and air quality.

Section B [15 marks]
Answer any one question in this section.

7(a) A school committee consisting of 3 people will be chosen at random from 5
male teachers and 3 female teachers. If X represents the number of male
teachers selected,
(i) Tabulate the probability distribution of X.
(ii) Find the mean and variance of X.
If Y represents the number of female teachers selected, hence, determine the [8 marks]
mean and variance for Y.

(b) The lifespan, in months, of a type of bulb is a random variable X. The probability

density function is given by

f (x) = 1 xe −x , x0
9 3

0 , x  0

Find the cumulative distribution function of X.

Hence, determine the probability that a randomly chosen bulb has a lifespan of [7 marks]

more than 8 months.

8.(a) The age, X, in years, in years at last birthday, of 250 mothers when their first baby

was born is given in the following tables.
x 18 − 20 − 22 − 24 − 26 − 28 − 30 − 32 − 34 − 36 − 38 −

Number

of 14 36 42 57 48 26 17 7 2 0 1

mother < 20 [5 marks]
‘18 –‘ means 18 [4 marks]

(i) Calculate the unbiased estimates of the mean and the standard deviation of X.

(ii) If the 250 mothers are a random sample from a large population, find 95%

confidence interval limits for the mean age of the total population.

(b) It is known that the tail lengths of a certain species of squirrel have mean14.0 cm
and standard deviation 3.8 cm. A zoologist takes a random sample of 20 squirrels
from the same species on an island and measure their tail lengths. She carry out a

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test, at the 5% significance level, of whether squirrels on the island have the same [1 mark]
mean tail.
[3 marks]
(i) State appropriate hypothesis for the test. [2 marks]
(ii) Determine the range of x , where x is the sample mean tail length, which the

null hypothesis would not be rejected.
(iii) State the conclusion of the test in the case where x =15.8

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