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 527. 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 577?

(b)

What percentage of students have an SAT math score greater than 627?

(c)

What percentage of students have an SAT math score between 477 and 527?

(d)

What is the z-score for student with an SAT math score of 630?

(e)

What is the z-score for a student with an SAT math score of 395?

(a)

What percentage of students have an SAT math score greater than 577?

(b)

What percentage of students have an SAT math score greater than 627?

(c)

What percentage of students have an SAT math score between 477 and 527?

(d)

What is the z-score for student with an SAT math score of 630?

(e)

What is the z-score for a student with an SAT math score of 395?

Explanation / Answer

a) as from normal distribution z =(X-mean)/std deviation

henc eP(X>577) =1 -P(X<577) =1-P(Z<(577-527)/50) =1-P(Z<1) =1-0.8413 =0.1587

hence 15.87%

b)P(X>627)

=1 -P(X<627) =1-P(Z<(627-527)/50) =1-P(Z<2) =1-0.97725 =0.02275

hence 2.275%

c)P(477<X<527) =P(-1<Z<0) =0.5-0.1587 =0.3413

d)zscore =(630-527)/50 =2.06

e)zscore =(395-527)/50 =-2.64

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