Sampling Distribution 2016-2017

The sampling distribution of a statistic is the distribution of all possible values that can be assumed by some statistic, computed from samples of the same size randomly drawn from the same population. 
Construction of sampling distributions :
1.  From a finite population of size N, randomly draw all possible samples of size n. 2.  Compute the statistic of interest for each sample.3.  Create a frequency distribution of the statistic.
We are interested in knowing three things about sampling distribution include (the mean, the variance and appearance of the graph (functional form of a sampling distribution).
When sampling is from a normally distributed
population, it can be shown that the distribution
of the sample mean will have the following properties:
1. The distribution of the will be normal.
2. The mean of the means of the samples will be equal to the mean of population from which the samples were drawn.
3.The variance of the distribution of will be
equal to variance of the population divided by sample size.
If the cranial length of certain large human
population is normally distributed with a mean
=185.6 mm, and standard deviation=12.7 mm.
what is the probability that a random sample of
size 10 from this population will have a mean
greater than 190 mm? P(z< 1.1) = 0.8643, P(z< -2.99) = 0.0014 , P (z< 2.99)= 0.9986