Statistics And Probability Question 397
Question: In a binomial distribution, the mean is 4 and the variance is. What is the mode?
Options:
A) 6
B) 5
C) 4
D) 3
Show Answer
Answer:
Correct Answer: C
Solution:
[c] AS give, $ np=4 $ and $ npq=3 $ [where p is the probability of success and q is the probability of failure for an event to occur, and ?n? is the number of trials]
$ \Rightarrow q=\frac{npq}{np}=\frac{3}{4} $ Also, $ p=1-q=1-\frac{3}{4}=\frac{1}{4} $
$ \therefore n=16 $ In a binomial distribution, on the value of r for which $ P(X=r) $ is maximum is the mode of binomial distribution. Hence, $ (n+1)p-1\le r\le (n+1)p $
$ \Rightarrow \frac{17}{4}-1\le r\le \frac{17}{4}\Rightarrow \frac{13}{4}\le r\le \frac{17}{4} $
$ \Rightarrow 3.25\le r\le 4.25 $
$ \Rightarrow r=4 $
BETA
