Answer:
Mean: 0.400
Standard error: 0.022
Step-by-step explanation:
We are taking samples of size n=500 out of a population with parameter p=0.40.
The expected distribution is the sampling distribution of sampled proportions. This distribution has parameters that are calculated as:
Mean: the mean of the sampling distribution is equal to the population proportion, as it is not biased.
In this case, the mean of this sampling distribution is p=0.40.
Standard error: the standard error depends on the population proportion and the sample size. It is calculated as:
![\sigma_p=\sqrt\dfrac{p(1-p)}{N}}=\sqrt\dfrac{0.4*0.6}{500}}=\sqrt{0.00048}=0.022](https://tex.z-dn.net/?f=%5Csigma_p%3D%5Csqrt%5Cdfrac%7Bp%281-p%29%7D%7BN%7D%7D%3D%5Csqrt%5Cdfrac%7B0.4%2A0.6%7D%7B500%7D%7D%3D%5Csqrt%7B0.00048%7D%3D0.022)
being p: population proportion, N: sample size.