A random sample of n measurements is drawn from a binomial population with probability of success . 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.

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.

Mean = 33.2000

Standard deviation = 4.4632

Step-by-step 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