Question

According to the American College Test (ACT), results from the 2004 ACT testing found that students had a mean reading score of 21.3 with a standard deviation of 6.0. Assuming that the scores are normal distributed: a. Find the probability that a randomly selected student has a reading, ACT score less than 20 Answer: b. Find the probability that a randomly selected student has a reading ACT score between 18 and 24. Answer: c. Find the probability that a randomly selected student has a reading ACT score greater than 30. Answer:

Answer 1

X has a normal distribution with u = 21.3,0 =6.0 6.0 6.0 a) P(x < 20) = P(*P < 20-21.3) =P(z<-0.22) =0.0.4129 (z value table) b) P(18<x<24)= P(1852.3 < * T4 < 24720.3)=P(-0.55<z <0.45) =P(z<0.45) –P9z<-0.55) =0.6736-0.2912 = 0.3824 (using z value table) c) P(x>30)=P(- > 30-21:3)=P(z>1.45)=1-P(251.45)=1-0.9265 =0.0735 (using z value table) a) Probability that a women professor makes more than the average men's salary Þ(x>147702) = P(x-L> 147702–159964)=P(2>-1.38)=1-P(25-1.38) 8900 =1-0.0838=0.9162 (using z value table) Using excel =1-NORMSINV(147702 – 159964) =0.91586 8900