# Sampling Distribution of the Sample Means from an Infinite Population

bunnypatotie
1. Individual students’ scores on a national test have a normal distribution with a mean of 18.5 and a standard deviation of 7.8. At a Trade School, 84 students took the test. If the scores at this school have the same distribution as national scores, what is the mean, standard deviation and variance of the sample mean for 84 students? Assume that in this case the population is infinite.

If, out of a population large enough to be treated as infinite with mean $$\displaystyle \mu$$ and standard deviation $$\displaystyle \sigma$$, a sample of size n is taken we can expect the sample to have mean $$\displaystyle \mu$$ and standard deviation $$\displaystyle \sigma \sqrt{n}$$.