The variance of a binomial distribution can be calculated using the formula:
Variance (σ²) = n * p * (1 – p)
In this formula:
- n represents the number of trials,
- p is the probability of success on each trial, and
- (1 – p) is the probability of failure.
For this particular case, you have:
- n = 100
- p = 0.20
Now, substituting these values into the variance formula:
- Variance = 100 * 0.20 * (1 – 0.20)
- Variance = 100 * 0.20 * 0.80
- Variance = 100 * 0.16
- Variance = 16
Thus, the variance of the binomial distribution with n = 100 and p = 0.20 is 16.
This means that in this distribution, the variability of the number of successes you might expect is quantified by the variance of 16, indicating a moderate spread around the mean number of successes.