Question

The distribution of grades in an introductory finance class is normally distributed, with an expected grade of 65. If the standard deviation of grades is 15, in what range would you expect 90 percent of the grades to fall?

Answer 1

The range in which 90% of class will fall will be (40.2,89.67)

Explanation:

Since the grades are normally distributed to obtain most possible range of grades obtained by the class we shall find the range of marks that give an area of 90% distributed equally about mean

These numbers shall correspond to

`Z_(1)=-1.6449\\\\Z_(2)=1.6449`

`Z_(1)=\frac{X-\bar{X}}{\sigma }\\\\X_(1)=\sigma Z_(1)+\bar{X}\\\\\therefore X_(1)=-1.6449* 15+65\\X_(1)=40.32\\Similarly\\\\X_(2)=\sigma Z_(2)+\bar{X}\\\\X_(2)=1.6449* 15+65\\X_(2)=89.67`