On a multiple choice test with 2222 questions, each question has four possible answers, one of which is correct. For students who guess at all answers, find the mean for the number of correct answers. Round to the nearest tenth. g

The mean for the number of correct answers is 5.5

Step-by-step explanation:

For each question, there are only two possible outcomes. Either it is guessed correctly, or it is not guessed correctly. The probability of a question being guessed 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:

22 questions

This means that

Each question has four possible answers, one of which is correct.

This means that

For students who guess at all answers, find the mean for the number of correct answers.

The mean for the number of correct answers is 5.5

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