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SSTS012 1)

Tutorial Questions 1

08/07/2019

Suppose there were only twelve students in supplementary exam of SSTS011 and the exam scores of these twelve students are as follows: Student #

1

2

3

4

5

6

7

8

9

1

11 11

Exam

5

7

3

8

4

6

2

5

8

0 6

5

3

mark

5

6

8

1

9

3

7

9

8

4

8

8

As a moderator of the module, use systematic random sampling to select a sample of size three. Start at student #2. 2)

3)

Use the exam mark of the students in 1) to calculate the following: i)

Sample mean.

ii)

Population mean.

iii)

Population standard deviation.

iv)

Population standard deviation of the sample mean. X

Suppose that

is a continuous random variable following the normal

distribution with mean E(Z) and 4)

Let

μ

and variance

σ

2

. If

Z=

X−μ , then find σ

Var (Z) .

x 1 , x 2 , ... , x n

be a random sample from a normal population with mean n

μ and variance 5)

2 σ >0 . If

The actual volume of soup in mean of

500 ml

´x =

xi ∑ i=1

E( ´x ) and

´ . Var (x)

n

1000 ml

and variance of

, then find

jars follows a normal distribution with

16 ml . If

X

denotes the actual volume

of soup in a jar. Calculate the following: i)

P(X > 496) .

ii)

P(X...