Probability
Binomial Distribution
MMTS_Full_Test_08
Grade 12
Question:
If $X$ follows binomial distribution with $n=8$ and $p=1/2$, then $P(|X-4|\le 2)$ is
$\dfrac{119}{128}$
$\dfrac{121}{128}$
$\dfrac{117}{128}$
$\dfrac{235}{256}$
Step-by-Step Solution
Key Concept: $P(2\le X\le 6)=\sum_{k=2}^{6}\binom{8}{k}(1/2)^8$
$\sum_{k=2}^{6}\binom{8}{k}=256-\binom{8}{0}-\binom{8}{1}-\binom{8}{7}-\binom{8}{8}=256-1-8-8-1=238$. $P=238/256=119/128$.
Correct Answer: 2