Let’s Summarize

• A standard normal distribution has a mean of 0 and a standard deviation of 1.
• A normal distribution is bell-shaped and the total area under the normal distribution curve is 1.
• A z-score measures how far X is from the mean in standard deviations. In other words, the z-score is the number of standard deviations X is from the mean of the distribution. For example, Z = 1 means the x-value is one standard deviation above the mean.
• We use a normal density curve to model the probability distribution for many variables, such as weight, shoe sizes, foot lengths, and other physical characteristics. For a normal curve, the empirical rule for normal curves tells us that 68% of the observations fall within 1 standard deviation of the mean, 95% within 2 standard deviations of the mean, and 99.7% within 3 standard deviations of the mean.
• Normal distribution tables and technology can be used to calculate probabilities of find percentiles associated with the normal distribution.