True or false question

If the population distribution is normal, then the sampling distribution of the sample mean(With sample size n) is normal. True or false.

A sampling distribution of a statistic is the distribution of values taken by the statistic in all possible samples of different sizes from the same population. True or false

For the same population a sampling distribution with greater size has greater standard distribution. True or false

The sampling distribution for a population depends on a fixed sample size . True or false

For sampling distributions of sample means for (normally distributed) population, a greater sample size leads to less concentration of the sample means around the population mean. True or false