# AP Statistics Curriculum 2007 Normal Critical

(Difference between revisions)
 Revision as of 18:51, 14 June 2007 (view source)IvoDinov (Talk | contribs)← Older edit Current revision as of 15:50, 3 May 2013 (view source)IvoDinov (Talk | contribs) m (→Textbook Prices) (12 intermediate revisions not shown) Line 1: Line 1: - ==[[AP_Statistics_Curriculum_2007 | General Advance-Placement (AP) Statistics Curriculum]] - Nonstandard Normal Distribution & Experiments: Finding Critical Values== + ==[[AP_Statistics_Curriculum_2007 | General Advance-Placement (AP) Statistics Curriculum]] - Non-Standard Normal Distribution and Experiments: Finding Critical Values== - === Nonstandard Normal Distribution & Experiments: Finding Scores (Critical Values)=== + === Non-Standard Normal Distribution and Experiments: Finding Scores (Critical Values)=== - Example on how to attach images to Wiki documents in included below (this needs to be replaced by an appropriate figure for this section)! + In addition to being able to [[AP_Statistics_Curriculum_2007_Normal_Prob | compute probability (p) values]], we often need to estimate the critical values of the Normal Distribution for a given p-value. -
[[Image:AP_Statistics_Curriculum_2007_IntroVar_Dinov_061407_Fig1.png|500px]]
+ - ===Approach=== + * The back and forth linear transformations converting between Standard and General Normal Distributions are always useful in such analyses (Let ''X'' denotes General ($X\sim N(\mu,\sigma^2)$) and ''Z'' denotes Standard ($Z\sim N(0,1)$) Normal random variables): - Models & strategies for solving the problem, data understanding & inference. + : $Z = {X-\mu \over \sigma}$ converts general normal scores to standard (Z) values. + : $X = \mu +Z\sigma \$ converts standard scores to general normal values. - * TBD + ===Examples=== + This [[Help_pages_for_SOCR_Distributions | Distributions help-page may be useful in understanding SOCR Distribution Applet]]. - ===Model Validation=== + ====[[SOCR_EduMaterials_Activities_Normal_Probability_examples | A large number of Normal distribution examples using SOCR tools is available here]]==== - Checking/affirming underlying assumptions. + - * TBD + ====Textbook Prices==== + Suppose the amount of money that college students spend each semester on textbooks is normally distributed with a mean of $195 and a standard deviation of$20. If we ask a random college students from this population how much she spent on books this semester, what is the maximum dollar amount that would guarantee she spends only as little as 30% of the population? ($P(X<184.512)=0.3$) +
[[Image:SOCR_EBook_Dinov_RV_Normal_013108_Fig12.jpg|500px]]

#### Human Weights and Heights

Human weights and heights are known to be approximately Normally distributed. Look at the SOCR Weighs and Heights Dataset and use the SOCR Charts to validate these statements based on this sample dataset.

• Suppose the heights of college women are approximately Normally distributed with a mean of 65 inches and a standard deviation of 2 inches. If a randomly chosen college woman is at the 10th percentile (shortest 10% for women) in height for college women, then what is the largest height closest to hers (i.e., what is her estimated height)?