Question

please help thank you in advance

It is reported that the ACT scores of freshman students at NMSU is approximately Normally distributed, with mean of 21.1 and standard deviation of 4.5. (1) (3pts) If the university decides to offer a scholarship to the top 3% of students, how high does a student need to score on ACT test to qualify for that scholarship? (No points will be given without proper steps) (2)(3pts) A math class has 30 freshmen enrolled. If we assume the 30 freshmen in the math class is a random sample, what is the chance that the AVERAGE ACT scores of the math class is below 20? (No points will be given without proper steps)

Answer 1

Let is random nariable the ACT scores Xn N(21.1,69.57?) We know that if xnN (M, 02) then. 2 = X-M ~ N(o,) 6 N(M, o 2 where n is sample size (1) Top 3% can be separated by score such that x so PCXX) = 0.03 P(x-21.1) X-21.1 -) = - 0.03 9.5 4.5 P(Z > 2e-21:1) =0.0 from 2-table calculator the zo score corresponding to probability 0.03 eis. 1.08 1 So x-21.1 9.5 = 1.881 HU x= 29.56 45

(2) Heru n=30 X~ N(21:1, (4:5)? - so 30 20-2101 < 05/30 P(x<20)=P 17-21.1 4.5/530 P(Z < -1:33 8877) From z-table 2-table calculator. P(X<20) = 0.090305 Ce