You are to take a multiple-choice exam consisting of 64 questions with 5 possible responses to each question. Suppose that you have not studied and so must guess (select one of the five answers in a completely random fashion) on each question. Let x represent the number of correct responses on the test. (a) What is your expected score on the exam? (Hint: Your expected score is the mean value of the x distribution.)(b) Compute the variance and standard deviation of x. Variance =Standard deviation

a) Expected score on the exam is 12.8.

b) Variance 10.24, Standard deviation 3.2

Step-by-step explanation:

For each question, there are only two possible outcomes. Either you guesses the answer correctly, or you does not. The probability of guessing the answer of a question correctly is independent of other questions. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

The variance of the binomial distribution is:

The standard deviation of the binomial distribution is:

64 questions.

So

5 possible answers, one correctly, chosen at random:

So

(a) What is your expected score on the exam?

(b) Compute the variance and standard deviation of x. Variance =Standard deviation

Variance 10.24

Standard deviation 3.2

its 0.1 miles per minute