I was doing a practice test and I got two questions wrong. The answer key said that these two statements were false:

As sample size increases, the standard deviation of the sampling distribution and the standard deviation of the population are increasingly similar.

-and-

For the standard normal curve, the area to the left of p=0.1 is the same as the area to the right of p=0.9

Can anyone tell me why these two statements are false?

Thank you!!