Suppose our final exam consists of 100 questions, each had 4 choices (A B C D) .

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Suppose our final exam consists of 100 questions, each had 4 choices (A B C D) . You are sure the correct answers for 60 questions, but the other 40, you completely have no idea. For those questions you pick randomly. Each question is 1 point and score for C or above is at leadt 75. What is your chance to get a C or better Suppose our final exam consists of 100 questions, each had 4 choices (A B C D) . You are sure the correct answers for 60 questions, but the other 40, you completely have no idea. For those questions you pick randomly. Each question is 1 point and score for C or above is at leadt 75. What is your chance to get a C or better

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Suppose our final exam consists of 100 questions, each had 4 choices (A B C D) . You are sure the correct answers for 60 questions, but the other 40, you completely have no idea. For those questions you pick randomly. Each question is 1 point and score for C or above is at least 75. What is your chance to get a C or better

The chance of choosing correct answers for the 40 questions is 0.25

n=40, p=0.25

We have to find P( x 15)

Using binomial distribution,

P(X=x) = (nCx) px (1-p)n-x

P( x 15) = 0.0544

or

Using normal approximation

Expectation = np = 10

Variance = np(1 - p) = 7.5

Standard deviation = 2.7386

With continuity correction, z = (14.5-10)/2.7386 =1.64

P( x 15)= P9 z>1.64)

=0.0505

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