Final answer:
To find the mean (μ) and standard deviation (σ) of a binomial distribution with n = 40 and p = 0.2, use the formulas μ = np for the mean and σ = √(npq) for the standard deviation. This gives a mean of 8 and a standard deviation of approximately 2.53.
Step-by-step explanation:
The question is asking about finding the mean and standard deviation for a binomial distribution with a given number of trials (n) and probability of success (p). Specifically, n = 40 and p = 0.2.
First, we calculate the mean, which is given by the formula μ = np. In this case:
Next, we calculate the standard deviation, which is the square root of the variance. The variance is calculated using the formula σ² = npq, where q is the probability of failure (1 - p).
- σ² = (40)(0.2)(1 - 0.2)
- σ² = 40(0.2)(0.8)
- σ² = 6.4
- σ = √6.4 ≈ 2.5298
Hence, for n = 40 and p = 0.2, the binomial distribution has a mean of 8 and a standard deviation of approximately 2.53.