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  4. A binomial variate X has mean = 6 and variance = 2 the probability that 5 le X le 7 is

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Q. A binomial variate X has mean = 6 and variance = 2 the probability that 5 $\le$ X $\le$ 7 is

Probability - Part 2

Solution:

Here mean = np = 6 ; variance = npq =2
$\therefore q = \frac{2}{6} = \frac{1}{3}; \therefore p = 1 - q = \frac{2}{3}; \therefore n = 9$
Now, probability of $ 5\le X \le7 $ is equal to $P\left(5\right) + P\left(6\right) + P\left(7\right) $
$ = ^{9}C_{5}p^{5}q^{4}+ ^{9}C_{6} p^{6}q^{3} + ^{9}C_{7} p^{7}q^{2} $