Question

Find the standard deviation of the binomial distribution for which n = 400 and p = 0.86. Provide an appropriate response. A test consists of 10 multiple choice questions, each with five possible answers, only one of which is correct. Find the mean and the standard deviation of the number of correct answers.

Answer 1

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.

Answer 2

To find the mean and standard deviation of the number of correct answers on a multiple-choice test, use the binomial distribution formula.

Step-by-step explanation:

To find the mean and standard deviation of the number of correct answers on a multiple-choice test, we can use the binomial distribution formula. Let's assume that the student randomly guesses for each question. In this case, the probability of getting a correct answer is 1/5, and the probability of getting an incorrect answer is 4/5.

The mean (µ) of the binomial distribution can be calculated as follows: µ = n * p, where n is the number of trials (10 questions) and p is the probability of success (1/5). Thus, µ = 10 * (1/5) = 2.

The standard deviation (σ) of the binomial distribution can be calculated as follows: σ = sqrt(n * p * (1-p)), where n is the number of trials (10 questions) and p is the probability of success (1/5). Thus, σ = sqrt(10 * (1/5) * (4/5)) ≈ 1.58.