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

Correct Answer: 96

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.