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.

center= (-2,0)

radius= sqrt2/2

step-by-step explanation:

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1