Complete question :
A random sample of n = 83 measurements is drawn from a binomial population with probability of success 0.4 . Complete parts a through d below. a. Give the mean and standard deviation of the sampling distribution of the sample proportion, . The mean of the sampling distribution of is nothing. The standard deviation of the sampling distribution of is nothing.
Answer:
Mean = 33.2000
Standard deviation = 4.4632
Explanation:
Given that :
Sample size (n) = 83
Probability of success (p) = 0.4
q = p' = (1 - p) = 1 - 0.4 = 0.6
The mean of the sampling distribution :
Sample size * probability of success
n * p = 83 * 0.4 = 33.2000
The standard deviation of the sampling distribution :
σ=√(sample size * probability of success * (1 - p))
σ = √n * p * (1 - p)
σ = √(83 * 0.4 * 0.6)
σ = √19.92
σ = 4.46318
σ = 4.4632