Question

**The answers in () were previously answered and are NOT correct

Suppose that the national average for the math portion of the College Board's SAT is 517. 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. If your answer is negative use “minus sign”.

(a) What percentage of students have an SAT math score greater than 592? (0.16 % is NOT correct)

(b) What percentage of students have an SAT math score greater than 667? (0.02 % is NOT correct)

(c) What percentage of students have an SAT math score between 442 and 517? (0.34 % is NOT correct)

Please explain. Thank you!

Answer 1

Solution :

Given that ,

mean = = 517

standard deviation = = 75

(a)

P(x > 592) = 1 - P(x < 592)

= 1 - P((x - ) / < (592 - 517) / 75)

= 1 - P(z < 1)

= 1 - 0.8413 = 0.1587

= 0.1587

Answer =15.87%

(b)

P(x > 667) = 1 - P(x < 667)

= 1 - P((x - ) / < (667 - 517) / 75)

= 1 - P(z < 2)

= 1 - 0.09772

= 0.0228

Answer = 2.28%

(c)

P(442 < x < 517) = P((442 - 517)/ 75) < (x - ) / < (517 - 517) / 75) )

= P(-1 < z < 0)

= P(z < 0) - P(z < -1)

= 0.5 - 0.1587

= 0.3413

Answer = 34.13%