In: Statistics and Probability

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 1310 on the SAT in 2010? (In other words, what ACT score is "equivalent" to an SAT score of 1310?) Round your answer to the nearest integer. b. What SAT score would place a student in the same percentile as a student who scored 14.6 on the ACT in 2010? (In other words, what SAT score is "equivalent" to an ACT score of 14.6?) Round your answer to the nearest integer.

**Solution:**

Given: ACT and SAT scores are both known to be normally distributed.

For the ACT :

μ=20 and σ=6.

For the SAT:

μ=1060 and σ=200.

**Part a.** What ACT score would place a student in
the same percentile as a student who scored 1310 on the SAT in
2010?

x = 1310 for SAT

Find z score for x = 1310

Now use this z score value to find corresponding ACT score:

Use following formula to find x value ( ACT score):

**ACT score would place a student in the same percentile
as a student who scored 1310 on the SAT in 2010 is 28**

**Part b)** What SAT score would place a student in
the same percentile as a student who scored 14.6 on the ACT in
2010?

x = 14.6 for ACT.

Find z score for x = 14.6

Now use this z score value to find corresponding SAT score:

Use following formula to find x value ( SAT score):

**Thus SAT score would place a student in the same
percentile as a student who scored 14.6 on the ACT in 2010 is
880.**

33. 2017 SAT scores All sections of the test are known to be
normally distributed with mean of approximately mean of 1060 and
standard deviation of 195
(a) Draw a normal curve with the parameters labeled.
(b) Shade the region that represents the proportion of test
takers who scored less than 1200.
(c) Suppose the area under the normal curve to the left of X =
1200 is 0.7636. Provide two interpretations of this result.

3) Scores on the SAT are normally distributed with a
mean of 500 and a standard deviation of 100
What is the probability of obtaining a score greater than
640?
What is the probability of obtaining a score less than
390?
What is the probability of obtaining a score between 725 and
800?
What is the probability of obtaining a score either less than
375 or greater than 650?
4) If you obtained a score of 75 on an test,...

The SAT scores for students are normally distributed with a mean
of 1000 and a standard deviation of 200. What is the probability
that a sample of 45 students will have an average score between 970
and 1010? Round your answer to 3 decimal places.

SAT verbal scores are normally distributed with a mean of 430 and a
standard deviation of 120 (based on data from the College Board
ATP). If a sample of 35 students are selected randomly, find the
probability that the sample mean is above 470.
A.) 0.244
B.) 0.9756
C.) 0.0445
D.) 0.0244

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

31. The 2018 Math Portion of the SAT scores are normally
distributed with a mean of 527 and a standard deviation of 117.
Give the range of scores that will satisfy the 68%, 95% and 99.7%
of the Empirical Rule.
32. Use the mean and standard deviation from #31 for the Math
Portion of the SAT. Suzette took the SAT in 2018 and scored higher,
on the Math Portion, than the bottom 30% but lower than the top 12%
of...

The SAT scores for US high school students are normally
distributed with a mean of 1500 and a standard deviation of
100.
1. Calculate the probability that a randomly selected student
has a SAT score greater than 1650.
2. Calculate the probability that a randomly selected student
has a SAT score between 1400 and 1650, inclusive.
3. If we have random sample of 100 students, ﬁnd the probability
that the mean scores between 1485 and 1510, inclusive.

The SAT scores earned on the math portion are approximately
normally distributed with mean 516 and standard deviation 116.
Answer the following questions based on this information. Make sure
you show your work.
1. Using a printout of the graph above or making your own copy,
mark the mean SAT score on the math proportion at the appropriate
place. Then mark values of score that are 1, 2, and 3 standard
deviations away from the mean value. Labeling your marks...

Scores on the SAT Mathematics test are believed to be normally
distributed. The scores of a simple random sample of five students
who recently took the exam are 570, 620, 710, 540 and 480. We want
to find a 95% confidence interval of the population mean of SAT
math scores.
A) Calculate the point estimate. (Round to four decimal places
as needed.)
B) Calculate the sample standard deviation. (Round to four
decimal places as needed.)
C) Calculate the standard error...

IQ scores are known to be normally distributed. The mean IQ
score is 100 and the standard deviation is 15. What percent of the
population has an IQ between 85 and 105. Need to solve it through
Excel

ADVERTISEMENT

ADVERTISEMENT

Latest Questions

- On Dr. Smith's Business Analytics exam, Mary had a z-score of 1.76. What percentage of students...
- Problem 12-23 Comprehensive Problem [LO12-1, LO12-2, LO12-3, LO12-5, LO12-6] Lou Barlow, a divisional manager for Sage...
- What are critical regions?
- Amdahl Corporation manufactures large-scale, high performance computer systems. In a recent annual report, the balance sheet...
- Define and write a sentence? What are the important mechanisms by which atoms are bonded?
- What are some reasons why household wealth might fluctuate even if current income is unaffected? Give...
- Data on the fuel economy of several 2010 model vehicles are given in the accompanying table....

ADVERTISEMENT