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  • 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 m

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____________.

Option: 1

0


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

\text { Variance }=20 \\

\Rightarrow \frac{\sum\left(x_{i}-\bar{x}\right)^{2}}{n}=20 \\

\mathrm{\Rightarrow \frac{\sum\left(x_{i}-62\right)^{2}}{7}=20} \\

\mathrm{\Rightarrow \sum\left(x_{i}-62\right)^{2}=140} \\

\mathrm{\Rightarrow \left(62-x_{1}\right)^{2}+\left(62-x_{2}\right)^{2}+ \ldots .+\left(62-x_{7}\right)^{2}=140}

Now if one student ( say x1 ) gets less than 50 marks then

\mathrm{\text { LHS }>12^{2}+\left(62-x_{2}\right)^{2}+\cdots+\left(62-x_{7}\right)^{2}} \\

\mathrm{\Rightarrow \text { LHS }>144}

In such a case LHS cannot equal \mathrm{RHS(=140)}

So, no student can fail

Hence answer is 0

Posted by

Gautam harsolia

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