Question

Find the mean, variance, and the standard deviation for the binomial distribution given n = 50 and p = 0.73. Express the mean in tenths like 12.3 and the variance and STD in thousandths.

a) Mean = 36.5, Variance = 9.161, STD = 3.026
b) Mean = 36.5, Variance = 6.255, STD = 2.504
c) Mean = 36.5, Variance = 4.258, STD = 2.064
d) Mean = 40.5, Variance = 5.458, STD = 2.334

Answer 1

The mean, variance, and standard deviation of a binomial distribution can be calculated using the formulas μ = n * p, σ² = n * p * q, and σ = √(Variance). For the given values of n = 50 and p = 0.73, the mean is 36.5, the variance is 9.161, and the standard deviation is 3.026.

Step-by-step explanation:

To find the mean, variance, and standard deviation of a binomial distribution, we use the following formulas:

Mean (μ) = n * p = 50 * 0.73 = 36.5

Variance (σ²) = n * p * q = 50 * 0.73 * 0.27 = 9.161

Standard Deviation (σ) = √(Variance) = √(9.161) ≈ 3.026

Therefore, the correct option is a) Mean = 36.5, Variance = 9.161, Standard Deviation = 3.026.