The distribution of SAT scores is normal with = 500 and = 100, Use the Standard

Question

The distribution of SAT scores is normal with = 500 and = 100, Use the Standard Normal Distribution tool to find the z-scores necessary to answering the following questions. To show the z-scores at enough precision, only the right tail from z = 0 to z = 2.4 is displayed. Standard Normal Distribution Mean = 0.0 Standard Deviation = 1.0 5000 .5000 0.0 0.0000 1.0 2.0 what SAT score (X value) separates the top 15% of the distribution from the rest? (Answer as a whole number.) What SAT score (X value) separates the top 10% of the distribution from the rest? (Answer as a whole number.) X= what SAT score (X value) separates the top 2% of the distribution from the rest? (Answer as a whole number.)

Explanation / Answer

= 500

= 100

Z = (X - ) /

a) Z value for top 15% :

P(Z > z) = 0.15

or, z = 1.04

SAT score = 500 + 1.04 * 100 = 604

b) Z value for top 10%:

P(Z > z) = 0.10

or, z = 1.28

SAT score = 500 + 1.28 * 100 = 628

c) Z value for top 2%:

P(Z > z) = 0.02

or, z = 2.05

SAT score = 500 + 2.05 * 100 = 705

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