Dear everyone

With all due respect, may I ask a help for some O/X quiz?

1)Suppose two random variables X and Y are negatively correlated. If X is above its mean, then Y is always below its mean.

(I know that when two are negatively correlated, if X gose up, Y goes down. However, I am not sure about the relation with mean)

2)Suppose X is a binomial random variable. Then 1000X is approximately a normal random variable.

(I know when n is bigger, it would be a normal distribution. However, I am not sure about 1000X..)

3)The polling agency should take a larger sample if the population is larger.

(I think that sample would be not affect whether the population is larger.. but not sure)

4)Linear regression framework can be applied to capture the decreasing marginal returns between two variables.

(I think it is O)

I deeply appreciate your help in advance.