Let a class have 20 students. The average marks of these students in the mathematics examination is 62 and their variance is 30.A student fails in the examination if he/she gets less than 40 marks, then the number of students that may fail can be equal to.

Variance  $30=\frac{{|x_1-62|}^2+{|x_2-62|}^2+{|x_3-62|}^2+\mathrm{.......}+{|x_{25}-62|}^2}{20}$
 $\Rightarrow {|x_1-62|}^2+{|x_2-62|}^2+{|x_3-62|}^2+\mathrm{.......}+{|x_{20}-62|}^2=600$
If one student gets less than 40
${|40-62|}^2={\left|22\right|}^2=484$ 
If two students fail
$2{|40-62|}^2=968>600$  Which is a contradiction
So, number of students that may fail is  $0or1$