The result of a Bus 220 exam yields a mean of 60 with a stan

The result of a Bus 220 exam yields a mean of 60 with a standard deviation of 4. What proportion of the class scored below 50 and above 70?

Solution

The result of a Bus 220 exam yields a mean of 60 with a standard deviation of 4.

let X be the random variable denoting the score of Bus 220 exam

so X~N(60,4²)

the proportion of class scored below 50 and above 70 is

P[X<50 and X>70]=1-P[50<X<70]=1-P[(50-60)/4<(X-60)/4<(70-60)/4]=1-P[-2.5<Z<2.5] where Z~N(0,1)

                         =1-[P[Z<2.5]-P[Z<-2.5]]=1-P[Z<2.5]+P[Z<-2.5]

                         =1-0.993790+0.0062097=0.0124197 [answer]   [using minitab]