Question

The sum and product of the mean and variance of a binomial distribution are 82.5 and 1350 respectively. Then the number of trials in the binomial distribution is _______.

Answer 1

Given that,
np + npq = 82.5 … (1)
np (npq) = 1350 … (2)
Since, Mean and Vairance be the roots of x2 – 82.5x + 1350 = 0
⇒ x2 – 22.5 x – 60x + 1350 = 0
⇒ x – (x – 22.5) – 60 (x – 22.5) = 0
Mean = 60 and Variance = 22.5
np = 60, npq = 22.5
$⇒q=\frac{9}{24}=\frac{3}{8},$
$⇒p=\frac{5}{8}$
$∴n\frac{5}{8}=60$
$⇒n=96$
So, the answer is 96.