Question

ACT and SAT scores are both known to be normally distributed. In 2017, the mean and standard deviation for the ACT were μ=20 and σ=6, respectively. The mean and standard deviation for the SAT were μ=1060 and σ=200, respectively.

a. What ACT score would place a student in the same percentile as a student who scored 1370 on the SAT in 2010? (In other words, what ACT score is "equivalent" to an SAT score of 1370?) Round your answer to the nearest integer.

b. What SAT score would place a student in the same percentile as a student who scored 15.8 on the ACT in 2010? (In other words, what SAT score is "equivalent" to an ACT score of 15.8?) Round your answer to the nearest integer.

Answer #1

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Data from a state indicate that scores on the SAT test are
normally distributed with a mean of 1089 and a standard deviation
of 199. Scores on the ACT test are normally distributed with a mean
of 19.1 and a standard deviation of 4.4. It is assumed that the two
tests measure the same aptitude, but use different scales.
If a student gets an SAT score that is the 58 percentile, find
the actual SAT score. Round answer to a...

Math part of SAT test scores has mean μ=500 and standard
deviation σ=100. ACT test scores have mean μ=18 and standard
deviation σ=6. Eleanor scored 680 on her SAT math test, Frodo
received score of 27 on his ACT test.
Assuming that both tests measured the same ability, who has a
better score.

Scores by women on the SAT-1 test are normally distributed
with a mean of 988 and a standard deviation of 202. Scores by women
on the ACT test are normally distributed with a mean of 20.9 and a
standard deviation of 4.6.
If a women gets a SAT score that is the 77th percentile, find
her actual SAT score and her equivalent ACT score.

Suppose that SAT math scores are normally distributed with a
mean of 516 and a standard deviation of 115, while ACT math scores
have a normal distribution with a mean of 22 and a standard
deviation of 5. James scored 650 on the SAT math and Jacob scored
29 on the ACT math. Who did better in terms of the standardized
z-score?
Group of answer choices
James
Jacob
They did relatively the same.
Impossible to tell because of the scaling

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 for more than 1 million students in a
recent high school graduating class was roughly normal with mean μ
= 20.8 and standard deviation σ = 4.8. SAT scores are reported on a
scale from 400 to 1600. The SAT scores for 1.4 million students in
the same graduating class...

High school students are faced with taking the ACT or
the SAT tests to measure their readiness to start college.
Quantitative SAT scores have a mean of 1525 and a standard
deviation of 305 while quantitative ACT scores have a mean of 25.1
and a standard deviation of 6.
a. A student takes the ACT and receives a score of 35
while another takes the SAT and receives a score of 2202. Which
student has scored higher relatively speaking?
b....

3. High school students are faced with taking the ACT or the SAT
tests to measure their readiness to start college. Quantitative SAT
scores have a mean of 1509 and a standard deviation of 312 while
quantitative ACT scores have a mean of 21.1 and a standard
deviation of 5.
a. A student takes the ACT and receives a score of
35 while another takes the SAT and receives a score of 2202. Which
student has scored higher relatively...

Problem 6.
Reports on a student's ACT or SAT usually give the percentile as
well as the actual score. With reference to problem 5 above,
suppose Jacob scores 16 on the ACT. What is his percentile? Show
your method.
Problem 5.
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 in
recent years has been roughly
Normal with mean...

The SAT scores for students are normally distributed with a mean
of 1050 and a standard deviation of 205. What is the probability
that a sample of 30 students will have an average score between
1030 and 1060? Round your answer to 3 decimal places.
Group of answer choices
0.058
0.309
0.583
0.761
0.691

A study was conducted on students from a particular high school
over the last 8 years. The following information was found
regarding standardized tests used for college admitance. Scores on
the SAT test are normally distributed with a mean of 998 and a
standard deviation of 203. Scores on the ACT test are normally
distributed with a mean of 20.7 and a standard deviation of 4.3. It
is assumed that the two tests measure the same aptitude, but use
different...

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