1. Sample Mean Distributions
Sample Means
Sample Mean Distributions

2. Sampling Distribution of the Mean
Suppose we draw all possible samples of size n from a population of size N. Suppose further that we compute a mean score for each sample. In this way, we create a sampling distribution of the mean.
We know the following. The mean of the population (μ) is equal to the mean of the sampling distribution (μx). And the standard error of the sampling distribution (σx) is determined by the standard deviation of the population (σ), the population size, and the sample size. These relationships are shown in the equations below:
      and     
Therefore, we can specify the sampling distribution of the mean whenever two conditions are met:
The population is normally distributed, or the sample size is sufficiently large.
The population standard deviation σ is known.

4. Tony makes a measurement in a bomb-making lab and records the result in his little
black book. The standard deviation of the experiment is 10 milligrams. Tony repeats
his experiment three times and records the mean of his three measurements.
What is the standard deviation of Tony’s mean result?
How many times must Tony repeat his experiment to reduce the standard
deviation to 3 milligrams?

5. The number of traffic accidents per week at an intersection varies with mean 2.2
and standard deviation 1.4. The number of accidents per week must be a whole
number, so the population is not normal.
If X is the mean number of accidents per week at the intersection during a year,
what is the distribution of X?
What is the approximate probability that is less than 2?
What is the approximate probability that there are fewer than 100 accident
at the intersection in a year?