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

Question

In some state the mean ACT score in Mathematics is ACT=20ACT=20 and the standard deviation is ACT=4,ACT=4, while the mean SAT score in Mathematics is SAT=490SAT=490 and the standard deviation is SAT=110.SAT=110. Suppose that the ACT scores and the SAT scores have a normal distribution. Terence gets a score of 19 on the Mathematics portion of the ACT and Philip gets a score of 394 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 28? Answer

(b) What proportion of SAT scores are greater than 490? Answer

(c) What proportion of ACT scores are between 8 and 20? Answer

(d) What proportion of SAT scores are between 160 and 600? Answer

(e) What is the z-score of Terence? Answer

(f) What is the z-score of Philip? Answer

(g) Who did better in Mathematics, Terence or Philip?

I need help solvng it with several decimal points

Explanation / Answer

a)

=20

=4

z=(x-)/

=(28-20)/4

=8/4

=2

P(x<28) =P(z<2) =0.9772

b)

=490

=110

z=(x-)/

=(490-490)/110

=0

p(x>490) =P(z>0) =0.5

c)

=20

=4

for x=8

z=(x-)/

=(8-20)/4

=-12/4

=-3

for x=20

z=(x-)/

=(20-20)/4

=0

P(8<x<20) =P(-3<z<0) =0.997/2 =0.4985   (because probability between 3 standard deviations is 99.7%)

d)

=490

=110

For x=160

z=(x-)/

=(160-490)/110

=-330/110

=-3

For x=600

z=(x-)/

=(600-490)/110

=110/110

=1

e)

For Terence

z=(19-20)/4

=-1/4

=-0.25

f) For Philip

z=(394-490)/110

=-96/110

=-0.87

g) since z score for Terence is more,hence Terence did better in Mathematics

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.