# If X Follows a Binomial Distribution with Parameters N = 8 and P = 1/2, Then P (|X − 4| ≤ 2) Equals(A)118 128(B) 119 128c) 117 128(D) None of These - Mathematics

#### Question

If X follows a binomial distribution with parameters n = 8 and p = 1/2, then P (|X − 4| ≤ 2) equals

##### Options
• $\frac{118}{128}$

• $\frac{119}{128}$

• $\frac{117}{128}$

• None Of these

#### Solution

$\frac{119}{128}$

$n = 8, p = \frac{1}{2}$
$\therefore q = 1 - \frac{1}{2} = \frac{1}{2}$
$\text{ Hence, the distribution is given by }$
$P(X = r) =^{8}{}{C}_r \left( \frac{1}{2} \right)^r \left( \frac{1}{2} \right)^{8 - r}$
$P\left( \left| X - 4 \right| \right) \leq 2$
$= P( - 2 \leq X - 4 \leq 2)$
$= P(2 \leq X \leq 6)$
$= P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)$
$= \frac{^{8}{}{C}_2 + ^{8}{}{C}_3 + ^{8}{}{C}_4 + ^{8}{}{C}_5 + ^{8}{}{C}_6}{2^8}$
$= \frac{28 + 56 + 70 + 56 + 28}{256}$
$= \frac{238}{256}$
$= \frac{119}{128}$

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#### APPEARS IN

RD Sharma Solution for Mathematics for Class 12 (Set of 2 Volume) (2018 (Latest))
Chapter 33: Binomial Distribution
MCQ | Q: 14 | Page no. 28

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If X Follows a Binomial Distribution with Parameters N = 8 and P = 1/2, Then P (|X − 4| ≤ 2) Equals(A)118 128(B) 119 128c) 117 128(D) None of These Concept: Bernoulli Trials and Binomial Distribution.