Probability Question 321
Question: If X follows a binomial distribution with parameter n=8 and $ p=\frac{1}{2} $ , then $ P(| X-4 |\le 2) $ is
Options:
A) $ \frac{119}{128} $
B) $ \frac{119}{228} $
C) $ \frac{19}{128} $
D) $ \frac{18}{128} $
Show Answer
Answer:
Correct Answer: A
Solution:
We have, $ P(| X-4 |\le 2)=P(-2\le X-4\le 2)=P(2\le X\le 6) $
$ =1-[P(X=0)+P(X=1)+P(X=7)+P(X=8)] $
$ =1-[ ^{8}C_0{{( \frac{1}{2} )}^{8}}{{+}^{8}}C_1{{( \frac{1}{2} )}^{8}}{{+}^{8}}C_7{{( \frac{1}{2} )}^{8}}{{+}^{8}}C_8{{( \frac{1}{2} )}^{8}} ] $
$ =1-{{( \frac{1}{2} )}^{8}}(1+8+8+1)=1-\frac{18}{2^{8}}=\frac{119}{128} $
BETA
