Find the mean and standard deviation for a binomial distribution with these values:
a. n = 1000, p = 0.3
b. n = 400, p = 0.01
c. n = 500, p = 0.5
To find the mean and standard deviation for a binomial distribution, you will need to use the formulas for these values. The formulas are as follows:
Mean (μ) = n * p
Standard Deviation (σ) = √(n * p * (1 - p))
Now let's calculate the mean and standard deviation for each scenario:
a. n = 1000, p = 0.3
Mean (μ) = 1000 * 0.3 = 300
Standard Deviation (σ) = √(1000 * 0.3 * (1 - 0.3)) ≈ 13.42
Therefore, the mean is 300 and the standard deviation is approximately 13.42.
b. n = 400, p = 0.01
Mean (μ) = 400 * 0.01 = 4
Standard Deviation (σ) = √(400 * 0.01 * (1 - 0.01)) ≈ 1.96
Therefore, the mean is 4 and the standard deviation is approximately 1.96.
c. n = 500, p = 0.5
Mean (μ) = 500 * 0.5 = 250
Standard Deviation (σ) = √(500 * 0.5 * (1 - 0.5)) = √(500 * 0.5 * 0.5) = √(125) = 11.18
Therefore, the mean is 250 and the standard deviation is approximately 11.18.
To find the mean and standard deviation for a binomial distribution, you can use the formulas mentioned above.