Consider a sampling distribution with p equals 0.12 and samples of size n each. Using the appropriate formulas, find the mean and the standard deviation of the sampling distribution of the sample proportion. a. For a random sample of size n equals 4000. b. For a random sample of size n equals 1000. c. For a random sample of size n equals 500.

a) Mean 0.12, standard deviation 0.0051

b) Mean 0.12, standard deviation 0.0103

c) Mean 0.12, standard deviation 0.0145

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean and standard deviation .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For proportions, the mean is , and the standard deviation is

In this problem, we have that:

So

a. For a random sample of size n equals 4000.

Mean 0.12, standard deviation

b. For a random sample of size n equals 1000.

Mean 0.12, standard deviation

c. For a random sample of size n equals 500.

Mean 0.12, standard deviation

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step-by-step explanation: