Question

Marks in an aptitude test given to $800$ students of a school was found to be normally distributed. $10\%$ of the students scored below $40$ Marks and $10\%$ of the students scored above $90$ marks. Find the number of students who scored between $40$ and $90$.

Answer 1

Let $X$ denote the height of the student given
$P(X<40)=10$ $\%$ $=\frac{10}{100}=0.1$
$P(X>90)=10$ $\%$ $=\frac{10}{100}=0.1$
$\therefore P(40<X<90)=P(-\infty <X<\infty )-\left\{P\right(X<40\left)P\right(X>90\left)\right\}$
$=1-0.1-0.1=0.8$
Out of $800$ students number of student scored between $40$ and $90$ $=800$ $\times$ $0.8=640$ students.