Step-by-step explanation:
The Standard Normal curve, shown here, has mean 0 and standard deviation 1. If a dataset follows a normal distribution, then about 68% of the observations will fall within of the mean , which in this case is with the interval (-1,1). About 95% of the observations will fall within 2 standard deviations of the mean, which is the interval (-2,2) for the standard normal, and about 99.7% of the observations will fall within 3 standard deviations of the mean, which corresponds to the interval (-3,3) in this case. Although it may appear as if a normal distribution does not include any values beyond a certain interval, the density is actually positive for all values, . Data from any normal distribution may be transformed into data following the standard normal distribution by subtracting the mean and dividing by the standard deviation .
Example:
The dataset used in this example includes 130 observations of body temperature. The MINITAB "DESCRIBE" command produced the following numerical summary of the data:
Variable N Mean Median Tr Mean StDev SE Mean
BODY TEMP 130 98.249 98.300 98.253 0.733 0.064
Variable Min Max Q1 Q3
BODY TEMP 96.300 100.800 97.800 98.700
