Next section: Difference between means

From a z table, it can be determined that 0.96
of the distribution is below 1.79. Therefore the probability that the mean
of 5 numbers will be greater than 580 is only 0.04. The calculation of the
probability with N = 10 is similar. The standard error of the mean (σm) is equal to :

which, of course, is smaller than the value
of 44.72 obtained for N=5.

Using the formula:

to calculate z and a
z table to calculate the probability, it can be determined that the
probability of obtaining a mean based on N = 10 that is greater than 580
is only 0.01. As expected, this is much lower than the probability of
.04 obtained for N = 5.

Summing up, finding an area under the sampling distribution of the
mean is the same as finding an area below any
normal curve. In this case, the normal curve is the sampling
distribution of the mean. It has a mean of μ and a standard deviation of

.

Next section: Difference between means