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~_________________________________
c) How many correct answers is this student expected to get( show some work, including what you entered into calculator)
d) What is the probability that the student correctly answers the expected number of correct questions
P(____)=_______________=________________
e) What is the probability that, by random guessing, the student passes the exam
P(____)=_______________=________________
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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.
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