The grades of an examination whose mean is 82 and whose standard ...

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The grades of an examination whose mean is 82 and whose standard deviation is 14 are normally distributed. The top 10 are to receive a special commendation. What score must be surpassed to receive this special commendation?

Question 2

The grades of an examination whose mean is 82 and whose standard deviation is 14 are normally distributed. Anyone who scores below 55 will be retested. What percentage does this represent?

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Answer to Question 1

The area to the right of z is 0.10, hence z = 1.28 . Then, 1.28 = (x  82)/14 . Solving for x, we get x = (1.28)(14) + 82 = 99.92.

Answer to Question 2

P(x < 55) = P(z < -1.93) = 0.5000  0.4732 = 0.0268