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Here is the problem:

In an exam with 15 multiple choice questions where each question has 4 choices (with only 1 correct choice), a student (who has not studied at all) is trying to answer the questions randomly. What is the chance that he answered between 2 to 4 questions correctly ? What is the variance of number of correctly answered questions?

Attempt : n= 15 , p= 1/4 need to find P (x is less than or equal to 4 or greater than or equal to 2)

Edit:

I have P(x=2) + P(x=3) + P (x=4)

(15 , 2)*(0.25)^2 (0.75)^13 + (15 , 3)(0.25)^3 * (0.75)^12 + ( 15 , 4)(0.25)^4 *(0.75)^11

Does that look right?

I also have the variance is npq so it should be (15* 0.25*0.75)

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    What have you tried? Where are you getting stuck? The numbers are small, so you can just compute everything explicitly...no need for any sort of approximation. – 2017-02-21
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    I figured out what I did wrong. – 2017-02-21

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