In some state the mean ACT score in Mathematics is ACT-20 and the standard devia

Question

In some state the mean ACT score in Mathematics is ACT-20 and the standard deviation is acr-4, while the mean SAT score in Mathematics is SAT-470 and the standard deviation is SAT distribution 90. Suppose that the ACT scores and the SAT scores have a normal Terence gets a score of 16 on the Mathematics portion of the ACT and Philip gets a score of 386 on the Mathematics portion of the SAT Answer questions (a)-(d) using the Empirical Rule. You should not use R here since the point of this exercise is to practice the Empirical Rule (a) What proportion of ACT scores are less than 12? (b) What proportion of SAT scores are greater than 380? (c) What proportion of ACT scores are between 12 and 32? (d) What proportion of SAT scores are between 200 and 740 (e) What is the z-score of Terence? (1) What is the z-score of Philip? (g) Who did better in Mathematics, Terence or Philip?

Explanation / Answer

a) P(X<12)=P(Z<(12-20)/4)=P(Z<-2)=0.025

b) P(X>380)=P(Z>(380-470)/90)=P(Z>-1)=0.84

c) P(12<X<32) =P(-2<Z<3)=0.9985-0.025=0.9735

d)P(200<X<740)=P(-3<Z<3)=0.997

e)z score of Terance =(16-20)/4=-1

f)z score of Philip=(386-470)/90=-0.933

g) Philip does better as his z score is relatively better

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