For a binomial random variable with n = 20 and p = 0.30, find the mean and standard deviation.

Step 1: Recall the mean formula for a binomial distribution.

For a binomial random variable:
μ = np

Step 2: Calculate the mean.

n = 20
p = 0.30

μ = 20(0.30)
μ = 6

Step 3: Recall the standard deviation formula.

For a binomial distribution:
σ = √(np(1 - p))

Step 4: Substitute the values.

σ = √(20(0.30)(0.70))

Step 5: Simplify.

20(0.30)(0.70) = 4.2

Therefore:
σ = √4.2
σ ≈ 2.05

Therefore, the mean is 6 and the standard deviation is approximately 2.05.