Question

In: Statistics and Probability

According to the College Board, scores on the math section of the SAT Reasoning college entrance...

According to the College Board, scores on the math section of the SAT Reasoning college entrance test in a recent year had a mean of 511 and a standard deviation of 119. Assume that they are roughly normal.

(a) What was the interval spanned by the middle 95% of SAT scores?

(b) How high must a student score to be in the top 16% of SAT scores?

Solutions

Expert Solution

solution:

middle 95% of score is

P(-z < Z < z) = 0.95

P(Z < z) - P(Z < -z) = 0.95

2 P(Z < z) - 1 = 0.95

2 P(Z < z) = 1 + 0. 95= 1.95

P(Z < z) = 1.95/ 2 = 0.975

P(Z <1.96 ) = 0.975

z  ±1.96

Using z-score formula  

x= z * +

x= ±1.96*119+511

x= 277.76 , 744.24

interval between 277.76 to 744.24

b.

P(Z > z) =16%

= 1 - P(Z < z) = 0.16

= P(Z < z ) = 1 - 0.16

= P(Z < z ) = 0.84

= P(Z < 0.99 ) = 0.84

z =0.99 (using standard normal (Z) table )

Using z-score formula  

x = z * +

x= 0.99*119+511

x= 628.81

x =623 rounded


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