Next section: Linear combination of means

The main difference between this problem and simple problems involving the area under the normal distribution is that in this problem you first had to figure out the mean and standard deviation of the sampling distribution of the difference between two means. In the simpler problems involving the area under the normal distribution, you were always given the mean and standard deviation of the distribution. The formula used there:

is used here in a different form:

.

Since the problem now concerns differences between means, the relevant statistic is the difference between means obtained in the sample (experiment), the relevant population mean (μ) is the mean of the sampling distribution of the difference between means, and the relevant standard deviation is the standard deviation of the sampling distribution of the difference between means.

Next section: Linear combination of means