Question

1) Suppose the scores on a Math exam and an English exam are both normally distributed, with the Math: N(60,20) and English (60,10). Barney gets an 80 on both tests.

a) On which test did he do better relative to his class mates?

b) How many students did better than Barney on each exam?

Answer 1

a)since z score =(X-mean)/standard deviation

z score for Math =(80-60)20 =1

z score for English =(80-60)10 =2

since z score is higher for english, Barney did better in English relative to his class mates

b)

for z =1, score , corresponding percentile =84.13%

therefore approx (100-84.13 =15.87%) of the students did better than Barney on Math

for z =2, score , corresponding percentile =97.72%

therefore approx (100-97.72 =2.28%) of the students did better than Barney on English

answered by: anonymous