The marks on a Statistics test are normally distributed with

The marks on a Statistics test are normally distributed with a mean of 62 and a variance of 225. If the instructor wishes to assign B\'s or higher to the top 30% of the students in the class, what mark is required to get a B or higher?

Solution

let X be the marks on statistics. so X~N(62,225=15²)

let K be marks required to get B or higher.

so P[X>K]=0.30

or, P[(X-62)/15>(K-62)/15]=0.30 or, P[Z>(K-62)/15]=0.30 or, 1-P[Z<(K-62)/15]=0.30 where Z~N(0,1)

or P[Z<(K-62)/15]=0.70=P[Z<0.524401] or, (K-62)/15=0.524401 or, K=69.866015 [answer]