STA1501/204/0/20
23
Tutorial letter 204/0/2023
Descriptive Statistics and Probability
STA1501
Year module
Department of Statistics
Solutions to Assignment 4
university
Define tomorrow. of south
africa
, SOLUTIONS TO ASSIGNMENT 04
Unique Nr.: 721906
Opening date: 15 June
Closing date: 12 july
PART A: 20 Marks
State whether the following statements are true or false.
QUESTION 1
Answer: True.
This is because there is an infinite number of possible values.
QUESTION 2
Answer: False.
In a normal distribution: the mean, median and mode are all at the same position on
the horizontal axis.
QUESTION 3
Answer: False.
The mean equals to zero is not a characteristic for a normal distribution.
QUESTION 4
Answer:
True.
µ = 18 and σ 2 = 9 than σ = 3.
x—µ 15 — 18
P (X ≥ 15) = P ≥ 15 =P Z ≥
σ 3
= P (Z ≥ —1.00)
= 0.1587.
2
, STA1501/204/0/20
23
QUESTION 5
Answer: False.
The probability to the right of z = 2.18 is 0.0146.
QUESTION 6
Answer: True.
● The total area under the curve equals to 1.
● The remaining area under the curve is 1 — 0.9904 = 0.0096.
● The value of z1 is equivalent to the corresponding 0.0096
value of to z1 = 2.59. = 0.0048 which corresponds
2
QUESTION 7
Answer: False.
Z is a standardized normal probability distribution.
P (Z = 2.10) = 0.
The probability of each individual value is zero in the case of continuous probability
distribution.
QUESTION 8
Answer: True.
Uniform distribution is a continuous probability distribution therefore the probability of
each individ- ual value is zero.
QUESTION 9
Answer: True.
QUESTION 10
Answer: False.
The standard
σ deviation of the sampling of the mean σ (from the original population).
x =
¯ ,
n
3
23
Tutorial letter 204/0/2023
Descriptive Statistics and Probability
STA1501
Year module
Department of Statistics
Solutions to Assignment 4
university
Define tomorrow. of south
africa
, SOLUTIONS TO ASSIGNMENT 04
Unique Nr.: 721906
Opening date: 15 June
Closing date: 12 july
PART A: 20 Marks
State whether the following statements are true or false.
QUESTION 1
Answer: True.
This is because there is an infinite number of possible values.
QUESTION 2
Answer: False.
In a normal distribution: the mean, median and mode are all at the same position on
the horizontal axis.
QUESTION 3
Answer: False.
The mean equals to zero is not a characteristic for a normal distribution.
QUESTION 4
Answer:
True.
µ = 18 and σ 2 = 9 than σ = 3.
x—µ 15 — 18
P (X ≥ 15) = P ≥ 15 =P Z ≥
σ 3
= P (Z ≥ —1.00)
= 0.1587.
2
, STA1501/204/0/20
23
QUESTION 5
Answer: False.
The probability to the right of z = 2.18 is 0.0146.
QUESTION 6
Answer: True.
● The total area under the curve equals to 1.
● The remaining area under the curve is 1 — 0.9904 = 0.0096.
● The value of z1 is equivalent to the corresponding 0.0096
value of to z1 = 2.59. = 0.0048 which corresponds
2
QUESTION 7
Answer: False.
Z is a standardized normal probability distribution.
P (Z = 2.10) = 0.
The probability of each individual value is zero in the case of continuous probability
distribution.
QUESTION 8
Answer: True.
Uniform distribution is a continuous probability distribution therefore the probability of
each individ- ual value is zero.
QUESTION 9
Answer: True.
QUESTION 10
Answer: False.
The standard
σ deviation of the sampling of the mean σ (from the original population).
x =
¯ ,
n
3
