The SAT scores earned on the math portion are approximately normally distributed with mean 516 and...

The SAT scores earned on the math portion are approximately normally distributed with mean 516 and standard deviation 116. Answer the following questions based on this information. Make sure you show your work.

1. Using a printout of the graph above or making your own copy, mark the mean SAT score on the math proportion at the appropriate place. Then mark values of score that are 1, 2, and 3 standard deviations away from the mean value. Labeling your marks with the corresponding scores.

2. Using the curve from question 1, shade the area under the curve that corresponds to P(X<500).

3. Find P(X<500). State in a sentence what this value represents in context of the data.

4. Using another version of the curve above, shade the area under the curve where X>600.

5. Find P(X>600). State in a sentence what this value represents in context of the data.

6. Find the probability that a test taker scores between 500 and 600.

7. If a test taker is at the 80th percentile, what is the score?

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