Answer to Question #332260 in Statistics and Probability for yvonne

Question

A teacher realizes that his students' marks on a statistic test are normally distributed with a mean of 62 and a standard deviation of 15. If the teacher wishes to assign minimum marks for grade B is referring to the top 30 per cent of the students' marks in the class, how many marks are required to get a minimum mark for grade B?

Answer 1

$\mu=62, \sigma=15.$

The 70th percentile of a normal distribution is $z=0.524\text{ (find from z-table)};$

$P(Z<0.524)=0.7;\\ P(Z>0.524)=1-0.7=0.3;\\ z=\cfrac{x-\mu}{\sigma};\\$

$x=z\sigma+\mu=0.524\cdot15+62=69.86.$

If marks are integers, than the minimum mark for grade B is 70.