Question

probability the average mark of a class of 100 students is over 80, if expectation is 75 and variance 9

Answer 1

Answer with explanation:

We want to calculate probability , in that case when

Average marks of 100 students = Over 80 = 80 + k

E(x)= 75

Variance (x)= 9

E(x²)=(80 +k)²

Variance (x)=E(x²)- [E(x)]²

⇒9=(80+k)²- (75)²

⇒6400 +k²+160 k-5625-9=0

⇒k²+160 k+366=0

⇒(k+80)² -6034=0

⇒(k+80)²=6034

$k=\sqrt{6034}-80\\\\ {\text{or}, k=-80-\sqrt{6034}$

Taking positive value of k, we get

k=77.68-80

k= -2.32

So, if, average marks of 100 students is over 80, and expectation is 75 and variance is 9,Then ,

Marks of each student should be around =80 -2.32=77.68

Required Probability

     $=\frac{\text{Average marks}}{\text{Total marks}}\\\\=\frac{77.68}{100}\\\\=0.7768$

     = 0.78 (Approx)