Question

A die is thrown 20 times. Getting a number greater than 4 is considered a success. Find the mean and variance of the number of successes.

Answer 1

Clearly, the distribution of the 'number of succeses' is a binomial distribution with n = 20 and,

$p=Probabilityofgettinganumbergreaterthan4=\frac{2}{6}=\frac{1}{3}$

Therefore,

$q=1-p=1-\frac{1}{3}=\frac{2}{3}$

Mean = np and Variance = npq

$Mean=20\times \frac{1}{2}=6.66$ and $Variance=20\times \frac{1}{3}\times \frac{2}{3}=4.44$

Hence, Mean = 6.66 and Variance = 4.44