AP Statistics: Section 2.2 B. The Standard Normal Distribution As the 68-95-99.7 Rule suggests, all Normal distributions share many common properties. In fact, all Normal distributions are the same if we measure in units of size with the mean as center. .
The Standard Normal DistributionAs the 68-95-99.7 Rule suggests, all Normal distributions share many common properties. In fact, all Normal distributions are the same if we measure in units of size with the mean as center.
If the variable we standardize has a Normal distribution, then so does the new variable z. This is true because standardizing is a linear transformation and does not change the shape of a distribution. This new distribution is called the
Standard Normal distribution.
The standard Normal distribution is a density curve. Any question about the proportion of observations can be answered by finding the area under the curve. Because all Normal distributions are the same when we standardize, we can find areas under any Normal curve from a table (or calculator).
Normal Distribution CalculationsWe can answer any question about proportions of observations in a Normal distribution by ____________ and then using the Standard Normal table.
Here is a recipe to do so.1. State the problem in terms of the observed variable x. Draw a picture of the distribution and _____the area of interest under the curve.2. Standardize x to restate the problem in terms of a standard Normal variable z. 3. Use the table or calculator and find the required area under the standard Normal curve.4. Write your conclusion in the context of the problem.
0.99% of all 14-year old boys have a cholesterol level of more than 240 mg/dl
49.7 % of 14-year old boys have blood cholesterol between 150 & 190 mg/dl
25% of 14-year old boys have blood cholesterol levels less than 149.9mg/dl