Question

Assume a binomial probability distribution has p = 0.80 and n = 300.

What are the mean and standard deviation?

Answer 1

The mean of a binomial distribution with p=0.80 and n=300 is 240, and the standard deviation is approximately 6.93.

Step-by-step explanation:

To calculate the mean and standard deviation of a binomial probability distribution with p = 0.80 and n = 300, you would use the formulas μ = np for the mean and σ = √npq for the standard deviation. In this case:

• The mean (μ) = 300 × 0.80 = 240
• The standard deviation (σ) = √(300 × 0.80 × 0.20) = √(300 × 0.16) = √48 ≈ 6.9282

Therefore, the mean number of successes is 240, and the standard deviation is approximately 6.93.