Problem 2-23 Suppose that the national average for the math portion of the Colle
ID: 2817163 • Letter: P
Question
Problem 2-23
Suppose that the national average for the math portion of the College Board's SAT is 534. 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 609? % (b) What percentage of students have an SAT math score greater than 684? % (c) What percentage of students have an SAT math score between 459 and 534? % (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?Explanation / Answer
1. Computation of percentage of students have an SAT math score greater than 609
Z = (Needed Score - Mean) / Standard Deviation = (609 - 534) / 75 = 1.0
Percentage of students = 0.50 - (0.6826 / 2)
Percentage of students = 0.50 - 0.3413
Percentage of students = 15.87%
2. Computation of percentage of students have an SAT math score greater than 684
Z = (Needed Score - Mean) / Standard Deviation = (684 - 534) / 75 = 2.0
Percentage of students = 0.50 - (0.9544 / 2)
Percentage of students = 0.50 - 0.4772
Percentage of students = 2.28%
3. Compuattion of percentage of students have an SAT math score between 459 and 534
p(459 <x<534) = P((459-534)/75 < x < (534 - 534)/75)
p(459 <x<534) = P(-1 < x < 0)
p(459 <x<534) = P(0 < x <1)
p(459 <x<534) = 34.13%
percentage of students have an SAT math score between 459 and 534 = 34.13%
4. the z-score for student with an SAT math score of 620
z- score = needed SAT - mean / SD
z- score = 620 - 534 / 75
z- score = 1.15
5. the z-score for student with an SAT math score of 405
z- score = needed SAT - mean / SD
z- score = 405 - 534 / 75
z- score = -1.72
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