Question

Suppose that the national average for the math portion of the College Board's SAT is 538. 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 638?
	%
(b)	What percentage of students have an SAT math score greater than 738?
	%
(c)	What percentage of students have an SAT math score between 438 and 538?
	%
(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?

Answer 1

(a)

= 538

= 100

To find P(X>638):

Z = (638 - 538)/100

= 1.00

Table of Area Under Standard Normal Curve gives area = 0.3413

So,

P(X>638) = 0.5 - 0.3413 = 0.1587

So,

Answer is:

0.1587

(b)

= 538

= 100

To find P(X>738):

Z = (738 - 538)/100

= 2.00

Table of Area Under Standard Normal Curve gives area = 0.4772

So,

P(X>638) = 0.5 - 0.4772 = 0.0228

So,

Answer is:

0.0228

(c)

= 538

= 100

To find P(438<X<538):

Z = (438 - 538)/100

= - 1.00

Table of Area Under Standard Normal Curve gives area = 0.3413

So,

P(438<X<538) = 0.3413

So,

Answer is:

0.3413

(d)

= 538

= 100

X = 620

Z = (620 - 538)/100

= 0.82

So,

Answer is:

0.82

(e)

= 538

= 100

X = 405

Z = (405 - 538)/100

= - 1.33

So,

Answer is:

- 1.33