Question

Suppose that the national average for the math portion of the College Board's SAT is 515....

Suppose that the national average for the math portion of the College Board's SAT is 515. The College Board periodically rescales the test scores such that the standard deviation is approximately 100. Answer the following questions using a bell-shaped distribution and the empirical rule for the math test scores.

If required, round your answers to two decimal places. If your answer is negative use “minus sign”.

(a) What percentage of students have an SAT math score greater than 615?
(b) What percentage of students have an SAT math score greater than 715?
(c) What percentage of students have an SAT math score between 415 and 515?
(d) What is the z-score for student with an SAT math score of 620?
(e) What is the z-score for a student with an SAT math score of 405?

Please show work. Can this be done using excel?

Homework Answers

Answer #1

(since we need to use empirical rule: for which 68%,95% and 99.7% values are within 1,2,3 standard deviaiton from mean , we should not use excel as it will give exact value)

for normal distribution z score =(X-μ)/σx
here mean=       μ= 515
std deviation   =σ= 100.000

a)

probability =P(X>615)=P(Z>(615-515)/100)=P(Z>1)=1-P(Z<1)=1-0.84 =0.16 ~ 16 %

b)

probability =P(X>715)=P(Z>(715-515)/100)=P(Z>2)=1-P(Z<2)=1-0.975 =0.025 ~ 2.5%

c)

probability =P(415<X<515)=P((415-515)/100)<Z<(515-515)/100)=P(-1<Z<0)=0.5-0.16=0.34 ~ 34%

d)

z score =(620-515)/100=1.05

e)

z score =(405-515)/100=-1.1

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Suppose that the national average for the math portion of the College Board's SAT is 512....
Suppose that the national average for the math portion of the College Board's SAT is 512. The College Board periodically rescales the test scores such that the standard deviation is approximately 100. Answer the following questions using a bell-shaped distribution and the empirical rule for the math test scores. If required, round your answers to two decimal places. If your answer is negative use “minus sign”. (a) What percentage of students have an SAT math score greater than 612? %...
Suppose that the national average for the math portion of the College Board's SAT is 514....
Suppose that the national average for the math portion of the College Board's SAT is 514. The College Board periodically rescales the test scores such that the standard deviation is approximately 75. Answer the following questions using a bell-shaped distribution and the empirical rule for the math test scores. If required, round your answers to two decimal places. (a) What percentage of students have an SAT math score greater than 589? % (b) What percentage of students have an SAT...
Suppose that the national average for the math portion of the College Board's SAT is 547....
Suppose that the national average for the math portion of the College Board's SAT is 547. The College Board periodically rescales the test scores such that the standard deviation is approximately 75. Answer the following questions using a bell-shaped distribution and the empirical rule for the math test scores. If required, round your answers to two decimal places. (a) What percentage of students have an SAT math score greater than 622? % (b) What percentage of students have an SAT...
A certain standardized​ test's math scores have a​ bell-shaped distribution with a mean of 515 and...
A certain standardized​ test's math scores have a​ bell-shaped distribution with a mean of 515 and a standard deviation of 105. Complete parts​ (a) through​ (c). ​(a) What percentage of standardized test scores is between 410 and 620​? ​(Round to one decimal place as​ needed.(b) What percentage of standardized test scores is less than 410 or greater than 620​? nothing​% ​(Round to one decimal place as​ needed.) ​(c) What percentage of standardized test scores is greater than 725​? nothing​% ​(Round...
Eleanor scores 680 on the math portion of the SAT. The distribution of math SAT scores...
Eleanor scores 680 on the math portion of the SAT. The distribution of math SAT scores is approximately Normal, with mean 500 and standard deviation 100. Jacob takes the ACT math test and scores 27. ACT math test scores are Normally distributed with mean 18 and standard deviation 6. a. Find the standardized scores (z-scores) for both students. b. Assuming that both tests measure the same kind of ability, who has the higher score? c. What score must a student...
Math SAT: Suppose the national mean SAT score in mathematics was 515. In a random sample...
Math SAT: Suppose the national mean SAT score in mathematics was 515. In a random sample of 40 graduates from Stevens High, the mean SAT score in math was 508, with a standard deviation of 35. Test the claim that the mean SAT score for Stevens High graduates is the same as the national average. Test this claim at the 0.10 significance level. (a) What type of test is this? This is a left-tailed test.This is a two-tailed test.     This is...
In a study of Math SAT scores done in 2010, the investigators computed the average Math...
In a study of Math SAT scores done in 2010, the investigators computed the average Math SAT score ( Ai )in each of the 50 states and D.C. and the percentage ( Pi ) of high school seniors in each state that took the test that year. They found that the correlation between the variables A and P was r = -0.77. (a) Does this mean that the test scores were better on average in states where fewer a lower...
The national average for the math portion of the College Board’s SAT is 521 with a...
The national average for the math portion of the College Board’s SAT is 521 with a standard deviation of 92. The median is 554. 1. What is the shape of the SAT math score distribution? Why? 2. _____________Rule predicts that __________percent of the SAT math score should lie between a 337 and 705, which are +/-___________ standard deviation(s) away from the mean.
In a study of Math SAT scores done in 2010, the investigators computed the average Math...
In a study of Math SAT scores done in 2010, the investigators computed the average Math SAT score ( Ai )in each of the 50 states and D.C. and the percentage ( Pi )of high school seniors in each state that took the test that year. They found that the correlation between the variables A and P was r = -0.77. (a) Does this mean that the test scores were better on average in states where fewer a lower percentage...
In a study of Math SAT scores done in 2010, the investigators computed the average Math...
In a study of Math SAT scores done in 2010, the investigators computed the average Math SAT score ( A i )in each of the 50 states and D.C. and the percentage ( P i )of high school seniors in each state that took the test that year. They found that the correlation between the variables A and P was r = -0.77. (a) Does this mean that the the test scores were better on average in states where fewer...