6.3 Applications of Normal Distributions Goal: At the end of this section I will have learned __________________________ _______________________________________________________________________________ (either the mean is not 0 or the standard deviation is not 1).

To work with nonstandard distributions, ________________________________________ ________________________________________________________________________________. To standardize values, use the following formula ______________________ Round z scores to __________________________________. The area in any normal distribution bounded by some score x is the same as ______ ________________________________________________________________________________. This means when working with a nonstandard normal distribution, ____________ ____________________________________________________________________________ ___________________________________________________________________________.

To find a probability in a nonstandard normal distribution follow these steps: 1. ____________________________________. a. Label the mean, the specific x values, and shade the region representing the desired probability. 2. ____________________________________________________________________________ __________________________________________________________________________. 3. ____________________________________________________________________________ __________________________________________________________________________.

Example: The level of cholesterol in the blood is cholesterol levels may increase the risk of heart blood cholesterol levels in a large population of is roughly Normal. For 14 year-old boys the mean standard deviation is  = 30 mg/dl. Levels above attention.

important because high disease. The distribution of people of the same age and sex is  = 170 mg/dl and the 240 mg/dl may require medical

What percent of 14-year old boys have more than 240 mg/dl of cholesterol?

What percent of 14 year-old boys have blood cholesterol between 170 and 240 mg/dl?

6.3 Applications of Normal Distributions To find a value from a known area follow these steps: 1. ___________________________________________________________________________. a. Label the given probability or percentage in the appropriate region of the graph and identify the x value(s) being sought. 2. ____________________________________________________________________________ ____________________________________________________________________________ ____________________________________________________________________________ ____________________________________________________________________________ 3. ____________________________________________________________________________ ____________________________________________________________________________

Example: Scores on the SAT Verbal test in recent years have followed an approximately normal distribution with  = 505 and  = 110. How high must a student score in order to place in the top 10% of all students taking the SAT?

What range of scores would put a student in the range of Q1 to Q3?