According to data from the 2010 United States Census, 64.2% of Americans in Susanville, CA were male. Suppose Maria, a researcher, takes a random sample of 100 Americans in Susanville and finds that 54 are male. Let ^ p represent the sample proportion of Americans in Susanville that were male. What are the mean and standard deviation of the sampling distribution of ^ p ? Provide your answer rounded to three decimal places.

The mean is 0.54 and the standard deviation is 0.05.

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 a sample proportion p in a sample of size n, the mean of the sampling distribution is p and the standard deviation is .

In this problem:

So

Mean 0.54

Standard deviation .

The mean is 0.54 and the standard deviation is 0.05.

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