Question

(S-AQ 3.60) There are two major tests of readiness for college: the ACT and the SAT. ACT scores are reported on a scale from 1 to 36. The distribution of ACT scores in recent years has been roughly Normal with mean µ = 20.9 and standard deviation s = 4.8. SAT scores are reported on a scale from 400 to 1600. SAT scores have been roughly Normal with mean µ = 1026 and standard deviation s = 209. The SAT scores that make up the top 12% of all scores range from to 1600. (Round your answer to the nearest whole number.)

Answer 1

Solution:-

Given that,

mean = = 1026

standard deviation = = 209

Using standard normal table,

P(Z > z) = 12%

= 1 - P(Z < z) = 0.12  

= P(Z < z) = 1 - 0.12

= P(Z < z ) = 0.88

= P(Z < 1.17 ) = 0.88  

z = 1.17

Using z-score formula,

x = z * +

x = 1.17 * 209 + 1026

x = 1270.53

SAT score = 1271