A test has 40 questions with 5 answer options each. If you guess at all 49 questions the mean and standard deviation of the number of correct answers are:

1 answer

The mean number of correct answers can be calculated using the formula for the expected value of a binomial distribution. Since there are 40 questions with 5 answer choices each, the probability of guessing correctly for each question is 1/5, and the expected value can be calculated as:

Mean = (Number of trials) * (Probability of success per trial)
= 40 * (1/5)
= 8

So, the mean number of correct answers is 8.

The standard deviation of a binomial distribution can be calculated using the formula:

Standard Deviation = √(Number of trials) * (Probability of success per trial) * (1 - Probability of success per trial)

Standard Deviation = √(40) * (1/5) * (4/5)
= √(8) * (4/25)
= √(32/25)
≈ 1.80

So, the standard deviation of the number of correct answers is approximately 1.80.