A Calculus student takes a 20question multiple choice test w

A Calculus student takes a 20-question, multiple choice test with 5 answer choices for each question. Find the mean and standard deviation of the number of questions that he/she gets correct.

Solution

No of questions = 20

No of choices for each question = 5

p = Prob for any question right = 1/5 = 0.2

As each question answer is independent of the other and also there are two outcomes, either right or wrong,
x- no of right questions follow a binomial distribution

n = No of trials = 20

p = 0.2

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Mean of x = np = 4

Var of x = npq = 0.8

Std dev of x = 0.8944