STA1501 ASSIGNMENT 3 SOLUTIONS 2023

Tutorial Letter 013/0/2023

Descriptive Statistics and Probability
STA1501

Year module


Department of Statistics


ASSIGNMENT 3 SOLUTIONS



Unique Nr.: 827246
Opening date: 29 May 2023
Due date: 12 June 2023




3

, PART A: 20 Marks

State whether the following statements are true or false.

QUESTION 1 [1 mark]

A random variable in a probability distribution can be either of a discrete type or of a continuous
type.

TRUE
A random variable in a probability distribution can be either of a discrete type or of a
continuous type. Discrete random variables can take on a finite number of distinct values
or a countable set of values, while continuous random variables can take on any value
within a specified range or interval. Examples of discrete random variables include the
number of children in a family or the outcome of a dice roll, while examples of continuous
random variables include height, weight, or time.



QUESTION 2 [1 mark]

The use of an appropriate probability distribution will enable you to determine the probability that
a discrete random variable will have a given value (integer) or a value in a given range.

TRUE. A discrete probability distribution is a probability distribution that shows the
likelihood of each possible value of a discrete random variable.



QUESTION 3 [1 mark]
The weight of a bag of potatoes in a supermarket represents a discrete random variable.
The number of years of schooling for employees of a company represents a continuous random
variable.

FALSE. Weight is quantitative continuous variable



QUESTION 5 [1 mark]

Consider a random variable X that takes the values 𝑥 = 4, 𝑥 = 8, or 𝑥 = 12, with the probabilities
are 0.2, 0.7 and 0.1, respectively. The mean of X is 7.6.
TRUE



4