Find the value of p, if the mean of the following distribution is 20.

It is given that,

Mean = 20

$\Rightarrow \frac{\sum f x}{N}=20$

$\Rightarrow \frac{5 p^{2}+100 p+295}{5 p+15}=20$

$\Rightarrow 5 p^{2}+100 p+295=20(5 p+15)$

$\Rightarrow 5 p^{2}+100 p+295=100 p+300$

$\Rightarrow 5 p^{2}=300-295$

$\Rightarrow 5 p^{2}=5$

$\Rightarrow p^{2}=1$

$\Rightarrow p=\pm 1$

Frequency can’t be negative.

Hence, value of p is 1.