Problem 2-23
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 math score greater than 697? %
(c) What percentage of students have an SAT math score between 472 and 547? %
(d) What is the z-score for student with an SAT math score of 625?
(e) What is the z-score for a student with an SAT math score of 415?
Supposing that the distribution of the students is normal, the mean of the distribution is given as and standard deviation is given as .
(a) A property of normal distribution is or , and since the distribution is symmetric, we have or . Putting the values of mean and SD, we have or . Hence, probability of students having score over 622 is 16%.
(b) Another property of normal distribution is or , and since the distribution is symmetric, we have or . Putting the values of mean and SD, we have or . Hence, probability of students having score over 697 is 2.5%.
(c) We have , and as the distribution is symmetric (around the mean), we have or . Putting the values of mean and SD, we have or . Hence, the probability of students having score between 472 and 547 is 34%.
(d) The z score would be or or or .
(e) The z score would be or or or .
Problem 2-23 Suppose that the national average for the math portion of the College Board's SAT...
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. A) What percentage of students have an SAT math score greater than 697?
Suppose that the national average for the math portion of the College Board's SAT is 517. The College Board periodically rescales the test scores such that the standard deviation is approximately 50. 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 567? % (b) What percentage of students have an SAT...
Problem 2-23 Suppose that the national average for the math portion of the College Board's SAT is 527. The College Board periodically rescales the test scores such that the standa 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 6027 (b) What percentage of students have an...
Suppose that the national average for the math portion of the College Board's SAT is 550. 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. If your answer is negative use “minus sign”. (a) What percentage of students have an SAT math score greater than 625? %...
Problem 2-23 Suppose that the national average for the math portion of the College Board's SAT is 518. 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 593? (b) What percentage of students have an...
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. B) What is the z-score for student with an SAT math score of 625?
Suppose that the national average for the math portion of the College Board's SAT is 526. 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. (a) What percentage of students have an SAT math score greater than 6267 3% (b) What percentage of students have an SAT...
Suppose that the national average for the math portion of the College Board's SAT is 548. 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. (a) What percentage of students have an SAT math score greater than 648? (b) What percentage of students have an SAT math...
The national average for the math portion of the College Board's SAT test 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. (a) What percentage of students have an SAT math score greater than 615? % (b) What percentage of students have an SAT math...
suppose that the national average for the math portion of the College Board's SAT is 522. 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. If your answer is negative use "minus sign (a) what percentage of students have an SAT math score greater than 597? (b)...