Assume that 1,000 people randomly solicited by mail from the general population

Question

Assume that 1,000 people randomly solicited by mail from the general population were given the same AS test and that the resulting scores were normally distributed around a mean of 6.0 with a standard deviation of 2.0. At what percentile would Students 1 and 6 from the current sample fall? Show how you derived your answers. (6 pts.) Describe in words what your answer to Question 8 means for Subject 1

         Student 1

         Student 6

students AS G 1 8 81 2 9 97 3 8 72 4 7 79 5 6 70 6 4 60 7 6 81 8 7 87 9 6 77 10 0 85 11 6 64 12 7 91 13 8 75 14 7 73 15 7 76 16 8 83 17 8 83 18 2 55 19 8 92 20 9 92 21 8 90 22 7 62 23 9 85 24 7 57 25 5 82 26 9 91 27 8 69 28 5 66 29 9 88 30 8 74

Explanation / Answer

here we use standard normal variate z=(x-mean)/sd

for student 1, the x=8, and z=(8-6)/2=1

P(z<1)=0.8413 ( using ms-excel=normsdist(1))

, so the percentile of student1 =84.13

for student 6, the x=84 and z=(4-6)/2=-1

P(z<-1)=0.1587, so the percentile of student6 =15.87

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