7.2 – Standard Units and Areas Under the Standard Normal Distribution Sam took a test and scored a 72 when the mean was 62. Teri took a test and scored a 52 when the mean was 42. Who did better compared to the other students and why?

If we could know the mean and standard deviation… Sam's mean was 62, if his standard deviation was 10, how many standard deviations to the right was he? Teri's mean was 42, if her standard deviation was 5, how many standard deviations to the right was she? Given the mean, µ, the score, x, and the standard deviation, ơ, what formula could tell you the number of standard deviations you are to the right/left of the mean?

Z- Score

Guided Exercise #3 As whole group, turn to page 258 – Look-over answers – Whole group clarification

Adjustment Remember???Adjustment Given an x distribution with a µ and ơ, the raw score, x, corresponding to a z-score is… x = z ơ + µ How? What does this look like?

Guided Exercise #4 As whole group, turn to page 259 – Look-over answers – Whole group clarification

Standard Normal Distribution Normal distribution (normal curve) with a mean µ = 0, and standard deviation ơ = 1 (Figure 7-12 on page 260) A normal distribution can be converted to the standard normal distribution by converting x values to their z values. (Figure 7-12 on page 260)

Area Under the Standard Normal Curve Sometimes we don’t have values that fall right on a standard deviation or a nice z-score, so we cannot use the Empirical Rule. Use a Standard Normal Distribution Table Appendix: Table 3 Lets look at this…

Guided Exercise #5 As whole group, turn to page 262 – Cover answers – Whole group clarification

How to use a left-tail style standard normal distribution table

Additional Information for z-table Treat any area to left of z value smaller than as Treat any area to left of z value greater than 3.49 as 1.000

Guided Exercise #6 As whole group, turn to page 265 – Cover answers – Whole group clarification

Checkpoint  Given mean and standard deviation, convert raw data to z scores  Given mean and standard deviation convert z scores to raw data  Graph the standard normal distribution and find areas under the standard normal curve.

Homework Read Pages – Take notes on what we have not covered Do Problems – Page (1-48) odds Check odds in back of book Read and preload 7.3 information – Notes/vocab