In a group of students the mean score for the SAT Math is 510 with a standard deviation of 95. The mean score for the SAT verbal is 490 with a standard deviation of 105.


a) Determine the mean combined score for this group of students.


b) Determine the combined standard deviation for this group of students.


c) What is the probability that one of these students achieves a combined score of 1400 or better?



I dont think you can add means together, obviously not if their standard deviations are different. Just dont know what to do on this one. Any help?

Let X be the random variable SAT math score and Y the random variable SAT verbal score.

Define U = X + Y.

(a) E(U) = E(X) + E(Y).

(b) IF X and Y are independent (a big IF but otherwise the question can't be answered) then Var(U) = Var(X) + Var(Y). Therefore sd(U) = ....

(c) You're probably meant to assume that X and Y follow a normal distribution. In which case U does to and has the above parameters. Calculate Pr(U > 1400).

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A) E(U) = 490+510 = 1000? combined mean = 1000?

b) Problem nowhere states anything about a normal curve or independent variables. So what should i do?

im still lost on b and c

You need to get clarification from your instructor (who will probably sat to make those assumptions). Assuming independence, the standard deviation is (as the formula I gave in my previous reply clearly says) .

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So now that I have the combined mean and combined standard deviation, can i just do another normal cdf for C?



normalcdf(1400,9999999,1000,141.59)

Yes. And actually sd = 141.60 if you're going to use 2 decimal place accuracy.

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.0023 or .23% that one of these students achieves a combined score of 1400 or better!

Woot. You should teach at my school.

I don't have the patience to teach. When I do teach it is to small children - they are still full of wonder, treat you with respect and awe, and don't worry about getting into medicine or law school when they leave school.

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If you're rounding to 4 decimal places then it's 0.0024.

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