AP Statistics Curriculum 2007 Normal Critical
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General Advance-Placement (AP) Statistics Curriculum - Nonstandard Normal Distribution & Experiments: Finding Critical Values
Nonstandard Normal Distribution & Experiments: Finding Scores (Critical Values)
In addition to being able to compute probability (p) values, we often need to estimate the critical values of the Normal distribution for a given p-value.
- The back and forth linear transformations converting between Standard and General Normal distributions are alwasy useful in such analyses (Let X denotes General () and Z denotes Standard () Normal random variables):
- converts general normal scores to standard (Z) values.
- X = μ + Zσ converts standard scores to general normal values.
Examples
This Distributions help-page may be useful in understanding SOCR Distribution Applet.
Textbook prices
Suppose the amount of money 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 he spent on books this semester, what is the maximum dollar amount that would guagantee she spends only as much as 30% of the population? (P(X < 184.512) = 0.3)
You can also do this problem exactly using the SOCR high-precision Nornal Distribution Calculator. If z_{o} = − 0.5243987892920383, then P( − z_{o} < Z < z_{o}) = 0.4 and P(Z<z_o)=0.3. Thus, x_{o} = μ + z_{o}σ = 195 + ( − 0.5243987892920383) * 20 = 184.512024214159234.
Height (in.) | 61.0 | 62.5 | 63.0 | 64.0 | 64.5 | 65.0 | 66.5 | 67.0 | 68.0 | 68.5 | 70.5 |
References
- Histogram plots
- Box-and-whisker plots
- Dotplot
- Quantile-Quantile probability plot
- SOCR High-Precision Normal Distribution Calculator
- SOCR Home page: http://www.socr.ucla.edu
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