(Solved): The sampling distribution of proportions describes how the sample proportions drawn from a populati ...

The sampling distribution of proportions describes how the sample proportions drawn from a population having proportion $p$ will vary from sample to sample. The standard deviation of the sampling distribution (called the standard error) is a way to measure sample-to-sample variability in the results. Suppose a sample of size $n$ is taken from a population where $p=0.76$. (a) For the given sample size, find the mean and standard error for the sampling distribution of proportions. Round all values to four decimal places. For a random sample of size $n=100$, the sampling distribution has a normal shape with center $p=$ and standard error $se=\sqrt{\left(\frac{p?(1?p)}{n}\right)}=$ For a random sample of size $n=500$, the sampling distribution has a normal shape with center and standard error (b) As the sample size increased from $n=100$ to $n=500$, the standard error of the sample proportion