### Question Description

## Final Answer

Again this is a question of binomial distribution.

in binomial distribution

P(x=K) = nCk * p^k * (1-p)^(n-k)

in this question

n=14

p=0.4

P(x>5) = 1 - P(x<=5)...Remember total probability is always equal to 1

P(x<=5) = P(1) + P(2) + P(3) + P(4) + P(5)

= 14C1 * 0.4^1 * 0.6^13 + 14C2 * 0.4^2 *0.6^12 + 14C3 * 0.4^3 * 0.6^11 + 14C4 * 0.4^4 *0.6^10 + 14C5 * 0.4^5 * 0.6^9

= 0.007+0.032+0.085+0.155+0.207

=0.485

*P(x>5) = 1 - P(x<=5)*

=1 - 0.485

=0.515

*Probability that more than 5 students smoke out of random sample of 14 students is 0.515*

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