You are to take a multiple-choice exam consisting of 64 questions with two possible responses to each question. Suppose that you have not studied and so must guess (select one of the two answers in a completely random fashion) on each question. Let x represent the number of correct responses on the test.(a) What kind of probability distribution does x haveb) Compare the variance and standard deviation of x.

x has a binomial distribution. The variance of x is 16 and the standard deviation is 4.

Step-by-step explanation:

For each question, there are only two possible outcomes. Either the person answer it correctly, or the person answers it wrong. The probability of answering 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 variance of the binomial distribution is:

The standard deviation of the binomial distribution is:

a) What kind of probability distribution does x haveb) Compare the variance and standard deviation of x.

Binomial

64 questions, so

Each question is guessed, out of two possible answers. So

x has a binomial distribution. The variance of x is 16 and the standard deviation is 4.

56.6

step-by-step explanation:

the ratio of the perimeters is equal to the scale.

the ratio of the areas is equal to the square of the scale.

34 / 20 = k

a / 19.6 = k²

substituting:

a / 19.6 = (34 / 20)²

a = 19.6 (34 / 20)²

a ≈ 56.6