This problem involves a binomial distribution because the student is randomly guessing on each multiple-choice question. We are interested in the probability of getting a question correct, which is $\frac{1}{5} = 0.20$, since each question has five possible choices.

Key assumptions:

• The number of questions is $n$.
• Each question is either answered correctly (with probability $p = 0.20$) or incorrectly (with probability $1 - p = 0.80$).
• The number of questions answered correctly $X$ follows a binomial distribution: $X \sim \text{Binomial}(n, p)$ where $n$ is the number of trials (questions), and $p$ is the probability of success (getting a question right).

The binomial distribution has the following properties:

• The expected value or mean, $\mu$, is: $\mu = np$
• The variance, $\sigma^2$, is: $\sigma^2 = np(1 - p)$
• The standard deviation, $\sigma$, is: $\sigma = \sqrt{np(1 - p)}$

However, without knowing the number of questions, $n$, we cannot compute these values explicitly. If you'd like to provide the number of questions, I can perform the calculation with exact values.

Would you like to provide the number of questions or proceed with further details based on this setup?

Follow-up questions:

1. How does the binomial distribution relate to this test-taking scenario?
2. What happens to the expected number of correct answers as $n$ increases?
3. How do we interpret the variance in the context of guessing on a test?
4. What are other methods to estimate the probability of success in multiple-choice questions?
5. How would these results change if the test had more than five choices per question?

Tip: In a binomial distribution, as the number of trials increases, the distribution starts to resemble a normal distribution due to the Central Limit Theorem.