Answer to Question #108375 in Statistics and Probability for Mohammed Moro

Question

If X is a binomial random variable with expected value 6 and variance 2.4. Find the probability of X=5.

Answer 1

$np=6$ and $npq=2.4$

Thus,$q=\frac{2.4}{6}=0.4$

$p=1-q=1-0.4=0.6$

$n=\frac{6}{0.6}=10$

Thus, $P(X=5)=\binom{10}{5}×0.6^5×0.4^5$

$=252×0.07776×0.01024=0.20066$

Similarly, the Excel formula =BINOM.DIST(5,10,0.6,FALSE) can be used to obtain the answer.