Normal distribution

An example from class

HEIGHTS OF MOTHERS CLASS LIMITS(in.)FREQUENCY TOTAL 1052 Example Of a Normal Variable

Normal distribution

Characteristics of normal distribution Symmetric, bell-shaped curve. Shape of curve depends on population mean (  ) and standard deviation (  ). Center of distribution is mean (  ) and mode and median. Spread is determined by standard deviation(  ). Most values fall around the mean, but some values are smaller and some are larger.

Examples of normal random variables testosterone level of male students head circumference of adult females length of middle finger of Stat/Soc students Height Weight IQ scores Body temperature Repeated measurement of same quantity

Probability between 65 and 70?

Probability above 75?

Probability below 65?

Normal Percents

The Rule

Example: Young Women’s Height The heights of young women are approximately normal with mean = 64.5 inches and std.dev. = 2.5 inches.

Example: Young Women’s Height % of young women between 62 and 67? % of young women lower than 62 or taller than 67? % between 59.5 and 62? % taller than 68.25?

Example: Young Women’s Height The heights of young women are approximately normal with mean = 64.5 inches and std.dev. = 2.5 inches.

Example: Young Women’s Height The heights of young women are approximately normal with mean = 64.5 inches and std.dev. = 2.5 inches.

Example: Young Women’s Height % of young women between 62 and 67? % of young women lower than 62 or taller than 67? % between 59.5 and 62? % taller than 68.25?

Working With the General Normal EXAMPLE: IQ Scores | 100 s.d. = 16 IQ Scores have a normal distribution with a mean of 100 and a standard deviation of 16. What is the 99% percentile of IQ Scores?

The Standard Normal Table: Table A Table A is a table of areas under the standard normal density curve. The table entry for each value z is the area under the curve to the left of z.