Question

find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p. where n = 50, p = 0.4

Answer 1

The mean (µ) of the binomial distribution is 20, the variance (σ²) is 12, and the standard deviation (σ) is approximately 3.464.

Step-by-step explanation:

To find the mean (µ), variance (σ²), and standard deviation (σ) of a binomial distribution, we can use the following formulas:
Mean (µ) = n * p
Variance (σ²) = n * p * q
Standard Deviation (σ) = √(n * p * q)
For the given values n = 50 and p = 0.4, we have:
Mean (µ) = 50 * 0.4 = 20
Variance (σ²) = 50 * 0.4 * (1 - 0.4) = 12
Standard Deviation (σ) = √(50 * 0.4 * (1 - 0.4)) ≈ 3.464