Module 4 Quiz

Test Your Discrete Probability Knowledge!

This quiz covers all topics from Module 4: Random Variables, Probability Distributions, Expected Value, Variance, and the Binomial Distribution. Pass with 70% (11/15 correct) to earn your Module 4 completion badge!

Quiz Rules

15 questions - Multiple choice
Passing score: 70% (11 out of 15 correct)
No time limit - Take your time and think carefully!
One attempt shown - But you can retake as many times as needed
Instant feedback - See explanations after submitting

1 Which of the following is a discrete random variable?

The height of a randomly selected student
The number of students in a class
The temperature in a room
The time it takes to run a mile

2 What must be true about the probabilities in any probability distribution?

All probabilities must be equal
All probabilities sum to 1.0
All probabilities must be between 0 and 0.5
Only the largest probability matters

3 Which statement best describes the expected value of a probability distribution?

The value that occurs most frequently
The long-run average value when the experiment is repeated many times
The spread or variability of the distribution
The same as the variance

4 Let X be the number of heads in two coin flips. What is E(X)?

5 What is the relationship between variance and standard deviation?

Variance = SD × SD (variance is the square of standard deviation)
SD = Variance × 2
They measure the same thing
Variance is always larger than SD

6 For a discrete distribution with values: P(X=1)=0.2, P(X=2)=0.5, P(X=3)=0.3, what is E(X)?

7 Which of the following is NOT a requirement for a binomial distribution?

Each trial has two possible outcomes (success or failure)
The probability of success changes from trial to trial
Trials are independent
The number of trials is fixed

8 What is the expected value of a binomial distribution with n=10 trials and p=0.4 success probability?

9 Which formula gives the variance of a binomial distribution?

Var(X) = n×p
Var(X) = n×p×(1-p)
Var(X) = n×(1-p)
Var(X) = p×(1-p)

10 A fair coin is flipped 20 times. What is the variance of the number of heads?

11 What does it mean if a binomial distribution is "symmetric"?

p is very small (less than 0.1)
p = 0.5
n is very large
The distribution shape doesn't matter

12 When is a binomial distribution approximately normal?

When n is large (typically n ≥ 30)
When np ≥ 10 and n(1-p) ≥ 10
Always, for any n and p
Only when p = 0.5

13 A quality control inspector finds that 3% of items are defective. If 50 items are checked, what is the expected number of defective items?

0.03
1.5
3
50

14 In the US household size example, if E(X) = 2.6 and Var(X) = 2.9, what is the standard deviation?

1.21
1.70
2.50
5.50

15 Which is the correct interpretation of "E(X) = 2.6 for US household size"?

The most common household size is 2.6 people
All households have exactly 2.6 people
On average, a randomly selected household has 2.6 people
The minimum household size is 2.6 people

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