Question

Us the following means and standard deviations: for ACT, µ=21, σ=3 and for SAT, µ=500, σ=100. (a) You take the ACT test and the SAT test. You get a 24 on the ACT and a 660 on the SAT. The college that you apply to only needs one score. Which do you want to send them (that is, which score is better: 24 or 660)? Why?

(b) What is the probability of having an ACT score of 20 or less?

(c) What SAT score do you need to have to be in the top 15% of the population?

(d) What is the probability of scoring between 500 and 650 on the SAT?

(e) What is your percentile rank if you have an ACT of 25.5?

Answer 1

solution Here for Act "=21, 6-3 for x=24, 2= *-4 = 24-2) = 1 for SAT, = 500, 2100 for x=660, 2= 66000 - 660-500 = 1.6 here a-score for SAT is more so, the SAT score of 660 is better b) fel 20, 2= 20-21 =-0-3333 P(x220)=P(22-0.3333) = 0-3695 c) The top ist means that bottom 85% then per the 2-score at 85% is 1.036 2= 1.036 x-500 = 1.036 x= 603-6 500-500 dy for soo, 2=500100 zo f& X=650, z = 6500600= 15 P (Between 500 8650)=P(soos aa 650) =P(0EZE15)=P/221.5) - P(220) = 0.9322-0.5=o. 4322 = 0.0332 e for at x =25.5, 2=25.5-21_1.5 P(&L 25.5)=P(2215) = 0.9332 = 193.32% the percentile rank is 93.32%