The standard deviation of a binomial distribution can be calculated using the formula:
σ = √(n * p * (1 – p))
Where:
- σ represents the standard deviation,
- n is the number of trials (in this case, 15),
- p is the probability of success on each trial (0.4),
- (1 – p) is the probability of failure, which would be 0.6.
Plugging the values into the formula:
σ = √(15 * 0.4 * 0.6)
Calculating:
- 15 * 0.4 = 6
- 6 * 0.6 = 3.6
- √(3.6) ≈ 1.897
Thus, the standard deviation of the binomial distribution when n = 15 and p = 0.4 is approximately 1.897.