SOLUTION: The SAT scores for MATH are normally distributed with a mean of 480 and a standard deviation of 80. If a test score is picked at random, find the probability that the score is: A)

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Question 543099: The SAT scores for MATH are normally distributed with a mean of 480 and a standard deviation of 80. If a test score is picked at random, find the probability that the score is:
A)greater than 400
Answer by jpg7n16(66) About Me  (Show Source):
You can put this solution on YOUR website!
We know that the following percentages hold true for standard deviation
1) avg +/- 1 stdv = 68% (34% each side of the avg)
2) avg +/- 2 stdv = 95% (47.5% each side of the avg)
3) avg +/- 3 stdv = 99.7% (49.85% each side of the avg)
So we start with the average: 480, and the stdv 80 - and we need to find which number we're dealing with.
A) greater than 400
-how many stdv away from the average is 400? 1. So we're dealing with the stats from #1 above.
Expressed as sections, here's how the percentages break out:
16% -(400)- 34% -(480)- 34% -(560)- 16%
What you need to do is either add all the % higher than 400, or take 100% - % below 400. Either way:
34%+34%+16% = 84%
100%-16% = 84%