Final answer:
The mean and standard deviation of the number of correct answers in the multiple choice test can be found using the properties of the binomial distribution.
Step-by-step explanation:
The mean (µ) of a binomial distribution is given by µ = np, where n is the number of trials and p is the probability of success.
In this case, there are 10 multiple-choice questions, so n = 10. The probability of getting a correct answer is 1/5, since there are five possible answers and only one is correct. Therefore, p = 1/5.
Substituting these values into the formula, we have µ = 10 * (1/5) = 2.
The standard deviation (σ) of a binomial distribution is given by σ = √(npq), where q = 1 - p.
In this case, q = 1 - (1/5) = 4/5.
Substituting these values into the formula, we have σ = √(10 * (1/5) * (4/5)) ≈ 1.2649.