Probability Question 333
Question: The mode of the binomial distribution for which mean and standard deviation are 10 and $ \sqrt{5} $ respectively is
Options:
A) 7
B) 8
C) 9
D) 10
Show Answer
Answer:
Correct Answer: D
Solution:
In binomial distribution, Mean = np = 10, variance = np(1-p) = 5
$ \therefore p=q=\frac{1}{2} $ Let x be the mode, then $ np-q < x < np+p $
$ \therefore 10+\frac{1}{2}>x>10-\frac{1}{2}\Rightarrow \frac{21}{2}>x>\frac{19}{2} $
$ \Rightarrow 9.5<x<10.5\Rightarrow x=10 $
BETA
