Question 600644
a)

Is this a binomial experiment? Yes


Explain how you know. Each guess at a question has two possible outcomes: A success (you get the question correct) or a failure (you get the answer wrong). Each guess is also independent of any other guess (assume that each question is unrelated to the other...ie no one question depends on another)



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b)


P(X = x) = (n C x)*(p)^(x)*(1-p)^(n-x)


P(X = 18) = (50 C 18)*(0.2)^(18)*(1-0.2)^(50-18)


P(X = 18) = (50 C 18)*(0.2)^(18)*(0.8)^(50-18)


P(X = 18) = (18053528883775)*(0.2)^(18)*(0.8)^32


P(X = 18) = (18053528883775)*(0.000000000000262144)*(0.00079228162514264337593543950336)


P(X = 18) = 0.00374957125234



So the probability of guessing exactly 18 questions correctly is approximately 0.00374957125234