# There are 80 questions from an SAT test, and they are all multiple choice with possible answers of a, b, c, d, e. For each question, only one answer is correct. Find the mean and standard deviation for the numbers of correct answers for those who make random guesses for all 80 questions.

Question
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There are 80 questions from an SAT test, and they are all multiple choice with possible answers of a, b, c, d, e. For each question, only one answer is correct. Find the mean and standard deviation for the numbers of correct answers for those who make random guesses for all 80 questions.

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Step 1

Define the random variable x as the number of correct answers. Here, the number of questions (n) is 80 and each question is independent of the other. Also, there are two possible outcomes (correct and wrong answers).

Step 2

For each question, the total number of choices is 5out of which, one option is the correct answer. The probability of success (p) is:

Step 3

Mean of the binomial dis...

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