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WorksheetsUnderstanding Random Variables and Distributions
Total questions: 14
Worksheet time: 7mins
Which of the following is an example of discrete random variable?
The number of heads in three coin flips.
The temperature at noon on a summer day.
The color of a car in a parking lot.
The height of a tree in a forest.
What is a continuous random variable? Provide an example.
A continuous random variable is a variable that is always constant. Example: the number of days in a week.
A continuous random variable can only take integer values. Example: number of students in a class.
A continuous random variable is a variable that can only take one specific value. Example: the color of a car.
A continuous random variable is a variable that can take any value within a given range. Example: height of individuals.
Calculate the probability of rolling a sum of 7 with two six-sided dice.
1/4
1/6
1/12
1/8
Identify whether the number of students in a classroom is a discrete or continuous random variable.
Continuous random variable
Variable with infinite values
Random variable with no specific count
Discrete random variable
Identify whether the height of students in a school is a discrete or continuous random variable.
Continuous random variable
Discrete random variable
Categorical random variable
Nominal random variable
If a random variable X follows a normal distribution with a mean of 10 and a standard deviation of 2, what is the probability that X is less than 8?
0.5000
0.0250
0.8413
0.1587
Convert the following value to a Z-score: 75, given a mean of 70 and a standard deviation of 5.
-1
0
1
2
What is the area under the standard normal curve to the left of Z = 0?
1.0
0.75
0.25
0.5
If a discrete random variable has the following probability distribution: P(X=1)=0.2, P(X=2)=0.5, P(X=3)=0.3, what is the probability of X being less than 2?
0.5
0.3
0.1
0.2
Calculate the probability of selecting a random number between 0 and 1 from a uniform continuous distribution.
-1
0.5
1
2
What is the Z-score for a value of 50 in a distribution with a mean of 40 and a standard deviation of 5?
-1
2
1
0
If the probability of a discrete random variable being 4 is 0.1, what is the probability of it being greater than 4?
0.5
0.2
0.1
0.9
In a normal distribution, what percentage of data falls within one standard deviation of the mean?
90%
68%
75%
50%
Identify a scenario where a continuous random variable is used in real life.
The type of fruit in a basket.
The height of adult males in a city.
The number of students in a classroom.
The color of a car in a parking lot.
