Question 712486
Each question of a forty-question multiple choice exam has 5 choices, only one of which is correct. Passing requires a minimum score of 70%. A student decides to answer each questions by randomly guessing.
a) In words, define the random variable
b) X = # of questions answered correctly
c) How many correct answers is this student expected to get( show some work, including what you entered into calculator)
mean = np = 40*(1/5) = 8
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d) What is the probability that the student correctly answers the expected number of correct questions 
P(x = 8)= 40C8(1/5)^8*(4/5)^32 = binompdf(40,1/5,8) = 0.1590
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e) What is the probability that, by random guessing, the student passes the exam
Note: 0.7*40 = 28
P(x >= 28) = 1 - P(40,1/5,27) = 1 - binomcdf(40,1/5,27) = 1.148x10^-11
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Cheers,
Stan H.