# Statistics

Students were given an exam with 300 multiple-choice questions. The distribution of the scores was normal and mean was 195 with a standard deviation of 30.

What were the scores of the students who were within one standard deviation of the mean?

What percent of students did that include?

What was the score of students who scored in the middle of the class? (50% did better, 50% did worse).

If A’s are given to students who score 90% or above, what is the minimum Z-score of someone getting an A?

Let’s say you got 235 on this test. Your colleague is in a different section of this course. Her score was 82 out of 100 on her test. In her section the mean was 72 and the standard deviation was 7. Which one of you did better?

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1. Z = (x - mean)/SD

Substitute known values to find x.

1. Find values in equation above for Z = ±1

2. Find Z scores in table (below) for both points between those points and the mean.

3. In normal distribution, mean = median = mode.

4. From table of "areas under normal distribution" in the back of your stats text, what Z score corresponds to .90 in larger area?

5. Compare your Z score with her Z score.

I hope this helps.

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