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Suppose $0.6$ of students submit assigned homework on time. In a typical class of $40$ students a professor has assigned homework. If a student submits homework on time, he gets $5$ points. Otherwise he gets $0$ points. Find the variance of the total number of points by all students.

So this is a binomial distribution. The variance is $40(0.6)(0.4)$?

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If $X$ is the total number of points by all students, write $X = \sum_{i=1}^{40} X_i$. I think we can use linearity now. – Naga Nov 19 '10 at 14:12
up vote 2 down vote accepted

Close, but the variance has to depend upon the number of points given. You have the variance in the number of students that turn in the work.

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So $T = 5I$ so that the variance is $5^{2}(0.4)(0.6)$. Hence it would be $(100)(25)(0.4)(0.6)$? – PEV Nov 19 '10 at 14:07
I don't understand where 100 came in the last expression. Your original 40*0.6*0.4 is the variance in the number of students turning in the work, and would be correct for the variance in score if the work was worth 1. You are right then to multiply by 5^2. But 5^2*40 does not equal 100*25 – Ross Millikan Nov 19 '10 at 14:56
Sorry was a typo. – PEV Nov 19 '10 at 16:45

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