To find the standard deviation of a binomial distribution, we can use the formula:
Standard Deviation (σ) = √(n * p * (1 – p))
In this case, we have:
- n = 15 (the number of trials)
- p = 0.4 (the probability of success)
First, we calculate (1 – p):
(1 – p) = 1 – 0.4 = 0.6
Now, we can plug the values into the formula:
σ = √(15 * 0.4 * 0.6)
σ = √(15 * 0.24)
σ = √(3.6)
σ ≈ 1.897
Therefore, the standard deviation of the binomial distribution is approximately 1.897.