Normal distribution An example from class Example Of

Normal distribution

An example from class

Example Of a Normal Variable HEIGHTS OF MOTHERS CLASS LIMITS(in. ) 52 -53 53 -54 54 -55 55 -56 56 -57 57 -58 58 -59 59 -60 60 -61 61 -62 62 -63 63 -64 64 -65 65 -66 66 -67 67 -68 68 -69 69 -70 70 -71 TOTAL FREQUENCY 0. 5 1 2 6. 5 18 34. 5 79. 5 135. 5 163 183 163 114. 5 78. 5 41 16 7. 5 4. 5 2 1052

Normal distribution

Characteristics of normal distribution • Symmetric, bell-shaped curve. • 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 • • • Weight of turtles IQ scores Body temperature Manufacturing (like size of lids) Probability (like how many heads out of 50 coin flips) • Repeated sampling (like if we asked 200 different people out of population same question)

The 68 -95 -99. 7 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 • 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 • 95% of all woman are between what heights?

Working With the General Normal EXAMPLE: 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? s. d. = 16 | 100

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.