For college-bound high school seniors from a certain Midwestern city, math score

Question

For college-bound high school seniors from a certain Midwestern city, math scores on the Scholastic Aptitude Test (SAT) averaged 480. with a standard deviation of 100. Assume that the distribution of math scores is bell shaped and symmetrical. What is the approximate percentage of scores that were between 380 and 580? What is the approximate percentage of scores that were above 680? Charlie scored 580 on the math portion of the SAT. What is the approximate percentage of students who scored lower than Charlie? Belly scored 680 on the math portion of the SAT. What is the approximate percentage of students w ho scored higher than Charlie hut lower than Betty?

Explanation / Answer

mean = 480 and std dev = 100

a) score between 380 and 580

For x = 380 , z = (380 - 480) /100 = -1 and for x = 580, z = (580 - 480) /100 = 1

Hence P(380 < x < 580) = P(-1 < z <1) = [area to the left of z = 1] - [area to the left of -1]

= 0.8413 - 0.1587 = 0.6825 = 68.25%

b) above 680

For x = 680, z = (680 - 480) / 100 = 2

Hence P(x > 680) = P(z > 2) = [total area] - [area to the left of -2.25]

= 1 - 0.9772 = 0.0228 = 2.28%

c)less then 580

For x = 580, the z-value z = (580 - 480) /100 = 1

Hence P(x < 580) = P(z < 1) = [area to the left of 1] = 0.8413 = 84.13%

d)less then 680

For x = 680, the z-value z = (680 - 480) / 100 = 2

Hence P(x < 680) = P(z < 2) = [area to the left of 2] = 0.9772 = 97.72%

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