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 544. 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.

What percentage of students have an SAT math score greater than 594?

What percentage of students have an SAT math score greater than 644?

(a)

What percentage of students have an SAT math score greater than 594?

(b)

What percentage of students have an SAT math score greater than 644?

(c) What percentage of students have an SAT math score between 494 and 544?

Explanation / Answer

Solution:

Given that

Mean = = 544

and standard deviation = 50

As we know that

( -1,+1) data within is 68%

( -2,+2) data within is 95%

( -3,+3) data within is 99.7%

(a)

students have an SAT math score greater than 594

Here z = (594 - 544)/50 = 1

P(x>594) = P(z>1) = 0.1587 = 15.87 %

(b) students have an SAT math score greater than 644

z = (644-544) /50 = 2

P(x>644) = P (z>2) = 0.0227 . = 2.27 %

(c) tudents have an SAT math score between 494 and 544?

z = (494-544) / 50 = -1

P(494 <x<544) = 34%

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