the sample mean and sample standard deviation on your econom

the sample mean and sample standard deviation on your economics examination were 60 and 20 respectively; the sample mean and sample standard deviation on your statistics examination were 55 and 10, respectively. You scored 70 on the economics exam and 62 on the statistics exam. Assuming that the two histograms of test scores are approximately normal histograms, (a)on which exam was your percentile score highest?, (b) approximate the percentage of the scores on the economics exam that were below your score. (c) approximate the percentage of the scores on the statistics exam that were below your score.

Solution

let X be the score in economics exam and Y be the score in statistics exam

given that X~N(60,20²)   and Y~N(55,10²)

in economics the score is 70   and in statistics the score is 62

a) Z score for economics score=(70-60)/20=0.5

    Z score for statistics score=(62-55)/10=0.7

so statistics score lies to the right of the economics score.

so the percentile score of statistics is higher. [answer]

b) P[X<70]=P[(X-60)/20<(70-60)/20]=P[Z<0.5] where Z~N(0,1)

                                                   =0.691462=69.1462% [answer]

c)P[Y<62]=P[(Y-55)/10<(62-55)/10]=P[Z<0.7]=0.758036=75.8036% [answer]