If the mean of a binomial distribution is 81, then find the interval in which standard deviation of the binomial distribution lies.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → $[0,9)$
Given mean = $np = 81$
∴ Standard deviation = $\sqrt{npq} = \sqrt{81q}=9\sqrt{q}$
$⇒ S.D. <9$
Also $S.D. ≥0$
$⇒ 0≤S.D. <9$
∴ Standard deviation lies in the interval $[0, 9)$.