NDA 2 2024 Maths, question 120

Topic: Probability

Q120

In a binomial distribution, if the mean is $6$ and the standard deviation is $\sqrt{2}$ , then what are the values of the parameters $n$ and $p$ respectively?

(a) $18\text{ and }1/3$
(b) $9\text{ and }1/3$
(c) $18\text{ and }2/3$
(d) $9\text{ and }2/3$ Correct answer

Solution.

Answer: (d) $9\text{ and }2/3$

For a binomial distribution, np=6 and np(1−p)=2.
Division gives 1−p=1/3, so p=2/3 and n=6/(2/3)=9.
Substitution yields variance 9(2/3)(1/3)=2, as required.