If the mean of a binomial distribution is 5 and its standard deviation is 2, then the number of trials is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 25
$\text{Mean} = np = 5$
$\text{Standard deviation} = \sqrt{npq} = 2$
$npq = 4$
$np = 5 \;\Rightarrow\; q = \frac{4}{5}$
$p = 1 - q = 1 - \frac{4}{5} = \frac{1}{5}$
$np = 5 \;\Rightarrow\; n \cdot \frac{1}{5} = 5$
$n = 25$
The number of trials is 25.