To find the mean of the number of correct answers, we need to find the probability of getting a single question correct and multiply it by the total number of questions, which is 40.
The probability of guessing a single question correctly is 1/5, since there are 5 answer options for each question.
Therefore, the mean of the number of correct answers is (1/5) * 40 = 8.
To find the standard deviation, we need to find the variance first.
The variance of the number of correct answers is given by the formula:
Variance = N * (p * (1 - p)),
where N is the total number of questions (40) and p is the probability of guessing a single question correctly (1/5).
The variance = 40 * ((1/5) * (1 - 1/5)) = 40 * (1/5) * (4/5) = 8 * 4/5 = 32/5.
The standard deviation is the square root of the variance. Therefore,
Standard deviation = sqrt(32/5) = sqrt(6.4) = 2.53 (rounded to two decimal places).
So, the mean and standard deviation of the number of correct answers when guessing at all 40 questions are approximately 8 and 2.53, respectively.
A test has 40 questions with 5 answer options each. If you guess at all 40 questions, the mean and standard deviation of the number of correct answers are
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