1. The z -score represents the number of standard deviations that a data value is from the mean. It is obtained by subtracting the mean from the data value and dividing this result by the standard deviation. The z-score is unitless with a mean of 0 and a standard deviation of 1.

2. Population Z - score Sample Z - score

3. EXAMPLE Using Z-Scores The mean height of males 20 years or older is 69.1 inches with a standard deviation of 2.8 inches. The mean height of females 20 years or older is 63.7 inches with a standard deviation of 2.7 inches. Data based on information obtained from National Health and Examination Survey. Who is relatively taller: Shaquille O’Neal whose height is 78 inches or Lisa Leslie whose height is 70 inches.

5. The maximum height is at the mean asymptotic – the tail never touches the base line and extends to infinity skewness is zero Kurtosis is mesokurtic Shaquille O’Neal’s height 99.81% of the cases are below Shaquille O’ Neil .19% of the cases are above Shaquille O’ Neil

9. Illustration for problem #1 1.78 – position of the student 96.16%=43 cases 3.84%=4 cases

11. Illustration for problem #2 .25 .0978 1.5 .4332 area away from the mean 33.54%

13. Illustration for problem #3 -0.75 .2734 -1.75 .4599 73.33% 22.56% 4%