The mean sat verbal score is 486, with a standard deviation of 95. use the empirical rule to determine what percent of the scores lie between 391 and 486. (assume the data set has a bell-shaped distribution.)

Find the z-scores for the two scores in the given interval.



For the score x =391, .

For the score x = 486,

Now you want the area (proportion of data) under the normal distribution from z = -1 to z = 0. The Empirical Rule says that 68% of the data falls between z = -1 to z = 1. But the curve is symmetrical around the vertical axis at z = 0, so the answer you want is HALF of 68%.

-2x+8=y=x-1
-2x+8=x-1
add 2x to both sides
8=3x-1
add 1
9=3x
divide 3
3=x
sub
y=x-1
y=3-1
y=2

(x,y)
(3,2)