Question

Suppose that the national average for the math portion of the College Board's SAT is 520. 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 595?

(b) What percentage of students have an SAT math score greater than 670?

(c) What percentage of students have an SAT math score between 445 and 520?

(d) What is the z-score for student with an SAT math score of 635?

(e) What is the z-score for a student with an SAT math score of 425?

Answer 1

let, X : SAT math score of students

X ~ N(520 , 75)

a). the probability of students have an SAT math score greater than 595 be:-

  ( from standard normal table)

so, the percentage of students have an SAT math score greater than 595 :-

= (0.1587*100)%

= 15.87 %

b).the probability of students have an SAT math score greater than 670 be:-

  ( from standard normal table)

so, the percentage of students have an SAT math score greater than 670 :-

= (0.0228*100)%

= 2.28 %

c).the probability of students have an SAT math score between 445 and 520 be:-

( from standard normal table)

so, the percentage of students have an SAT math score between 445 and 520 is:-

= (0.3413 *100 )%

= 34.13 %

d). the z-score for student with an SAT math score of 635 is:-

e) the z-score for student with an SAT math score of 425 is :-

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