SOLUTION: Scores on the SAT form a normal distribution with a mean score of 500 and a standard deviation of 100. Find the range of scores that defines the middle 80% of the distribution of S

Question 1202109: Scores on the SAT form a normal distribution with a mean score of 500 and a standard deviation of 100. Find the range of scores that defines the middle 80% of the distribution of SAT scores.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
mean is 500
standard deviation is 100
z-score with 10% area to the left of it is equal to -1.28
z-score with 90% area to the left of it is equal to 1.28
area in between is 80%.
raw score when z = -1.28 is given by:
-1.28 = (x - 500) / 100
solve for x to get x = -1.28 * 100 + 500 = 372
raw score when z = 1.28 is given by:
1.28 = (x - 500) / 100
solve for x to get x = 1.28 * 100 + 500 = 628
the range of scores that defines the middle 80% os from 372 to 628.
these are rounded numbers.
a more exact number would be 371.8448433 to 628.1881867.
round as required.

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