In R Language there are two major tests of readiness for col

In R Language, there are two major tests of readiness for college, the ACT and the SAT. ACT scores are

reported on a scale from 1 to 36. The distribution of ACT scores is approximately Normal

with mean = 21:5 and standard deviation = 5:4. SAT scores are reported on a scale

from 600 to 2400. SAT scores are approximately Normal with mean = 1509 and standard

deviation = 321.

(a) Isabella scores 1820 on the SAT. Jermaine scores 29 on the ACT. Assuming that both

tests measure the same thing, who has the higher score. Report the z-scores for both

students.

(b) Jose scores 2080 on the SAT. Assuming that both tests measure the same thing, what

score on the ACT is equivalent to Jose\'s SAT score?

(c) Reports on a students ACT or SAT usually give the percentile as well as the actual

score. Maria scores 2090 in the SAT. What is her percentile? Jacob scores 19 on the

ACT. What is his percentile?

(d) What SAT scores make up the top 10% of all scores? What SAT scores make up the

bottom 20% of all scores?

Solution

Sol:

ACT scores

mean:21.5

std dev=5.4

SAT scores

mean=1509

std dev=321

Sola:

SAT

isablla

Zi=x-mean/stddev

=1820-1509/321

=0.969

jermaine zscore Zj

Zj=29-21.5/5.4

=1.39

Jermaine has the higher z-score, and scores \"higher.\"

Solutionb:

Jose scores 2080 on the SAT. Assuming that both tests measure the same thing, what

score on the ACT is equivalent to Jose\'s SAT score

jose z score Zj=x-mean/sd

=2080-1509/321

=1.779

BOTH SCORES ARE EQAUL EQAUTE Z SCORE

Zsat=Z act

1.779=X-21.5/5.4

1.779*5.4+21.5=X

X=31.1066

X=31(rounding to nearest integer

31 score on the ACT is equivalent to Jose\'s SAT score of 2080

Solutionc:

z score of mnaria

Zm=x-mean./sd

=2090-1509/321

=1.8099

convert z score to perecentle.

96 perecntile

marias perecentile=96

similarly

jacobis score to z score

Zja=19-21.5/5.4

=-0.463=32 percentile.