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QJEEM22Mabe60: JEE Main 2022 Mathematics - Class 11 JEEM22Mabe60 Solution: Suppose a class has 7 students. The average marks of these…

Suppose a class has 7 students. The average marks of these students in the mathematics examination is 62, and their variance is 20. A student fails in the examination if he/she gets less than 50 marks, then in worst case, the number of students can fail is _________.

Step-by-Step Verified Solution

According to given data

∑i=17(xi−62)27=20{{\sum\limits_{i = 1}^7 {{{({x_i} - 62)}^2}} } \over 7} = 20

⇒∑i=17(xi−62)2=140\Rightarrow \sum\limits_{i = 1}^7 {{{({x_i} - 62)}^2} = 140}

So for any xi, (xi−62)2≤140{({x_i} - 62)^2} \le 140

\Rightarrow {x_i} > 50\,\forall i = 1,2,3,\,\,.....\,\,7

So no student is going to score less than 50.

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