Suppose that the national average for the math portion of the College Board\'s S

Question

Suppose that the national average for the math portion of the College Board's SAT is 529. 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 score. If required, round your answers to two decimal places. (a) What percentage of students have an SAT math score greater than 604? (b) what percentage of students have an SAT math score greater than 679? (c) What percentage of students have an SAT math score between 454 and 529? (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

We will use these params to solve the problem:

Mean = 529

Stdev = 75

a. P(X>604) = P(Z> 604-529 / 75) = P(Z>1) = .16 or 16% of the data has greater than 604

b. P(X>679) = P(Z> 679-529/75) = P(Z>2) = 1-.9772 = .0228

c. P(454<X<529) = P(-1<X<0) = .34

d. Z score for (620-529) / 75 = 1.213

e. Z score for 405 is (620-405)/75 = 2.87

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.