AP Statistics Curriculum 2007 Normal Critical - Revision history

Tdlee: Text replacement - "{{translate|pageName=http://wiki.stat.ucla.edu/socr/" to ""{{translate|pageName=http://wiki.socr.umich.edu/"

2020-03-03T18:04:28Z

Text replacement - "{{translate|pageName=http://wiki.stat.ucla.edu/socr/" to ""{{translate|pageName=http://wiki.socr.umich.edu/"

Dinov: /* Textbook Prices */

2014-10-06T21:22:15Z

‎Textbook Prices

IvoDinov: /* Textbook Prices */

2013-05-03T15:56:10Z

‎Textbook Prices

Jenny: /* Textbook Prices */

2010-06-28T20:00:10Z

‎Textbook Prices

IvoDinov: added a link to the Problems set

2009-10-26T04:57:49Z

added a link to the Problems set

IvoDinov: /* Human Weights and Heights */

2009-05-20T15:54:44Z

‎Human Weights and Heights

IvoDinov: /* Textbook Prices */

2009-05-20T15:52:12Z

‎Textbook Prices

IvoDinov: /* Non-Standard Normal Distribution and Experiments: Finding Scores (Critical Values) */ typo

2008-05-15T15:42:11Z

‎Non-Standard Normal Distribution and Experiments: Finding Scores (Critical Values): typo

PriscillaChui: /* General Advance-Placement (AP) Statistics Curriculum - Nonstandard Normal Distribution & Experiments: Finding Critical Values */

2008-03-01T22:07:10Z

‎ General Advance-Placement (AP) Statistics Curriculum - Nonstandard Normal Distribution & Experiments: Finding Critical Values

PriscillaChui: /* General Advance-Placement (AP) Statistics Curriculum - Nonstandard Normal Distribution & Experiments: Finding Critical Values */

2008-02-12T21:16:20Z

‎ General Advance-Placement (AP) Statistics Curriculum - Nonstandard Normal Distribution & Experiments: Finding Critical Values

← Older revision		Revision as of 18:04, 3 March 2020
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	* SOCR Home page: http://www.socr.ucla.edu		* SOCR Home page: http://www.socr.ucla.edu

−	{{translate\|pageName=http://wiki.~~stat~~.~~ucla~~.edu~~/socr~~/index.php?title=AP_Statistics_Curriculum_2007_Normal_Critical}}	+	"{{translate\|pageName=http://wiki.socr.umich.edu/index.php?title=AP_Statistics_Curriculum_2007_Normal_Critical}}

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 ====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? (<math>P(X<184.512)=0.3</math>)
+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? (<math>P(X<184.512)=0.3</math>)
 <center>[[Image:SOCR_EBook_Dinov_RV_Normal_013108_Fig12.jpg|500px]]</center>

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 <center>[[Image:SOCR_EBook_Dinov_RV_Normal_013108_Fig12.jpg|500px]]</center>
-You can also do this problem exactly using the [http://socr.ucla.edu/Applets.dir/Normal_T_Chi2_F_Tables.htm SOCR high-precision Nornal Distribution Calculator]. If <math>z_o=-0.5243987892920383</math>, then <math>P(-z_o<Z<z_o)=0.4</math> and P(Z<z_o)=0.3. Thus, <math>x_o=\mu +z_o\sigma=195+(-0.5243987892920383)*20=184.512024214159234.</math>
+You can also do this problem exactly using the [http://socr.ucla.edu/Applets.dir/Normal_T_Chi2_F_Tables.htm 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, \(x_o=\mu +z_o\sigma=195+(-0.5243987892920383)*20=184.512024214159234\).
 <center>[[Image:SOCR_EBook_Dinov_RV_Normal_013108_Fig13.jpg|500px]]</center>

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 ====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 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? (<math>P(X<184.512)=0.3</math>)
+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? (<math>P(X<184.512)=0.3</math>)
 <center>[[Image:SOCR_EBook_Dinov_RV_Normal_013108_Fig12.jpg|500px]]</center>

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 * 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 10<sup>th</sup> 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)?
 <center>[[Image:SOCR_EBook_Dinov_RV_Normal_013108_Fig14.jpg|500px]]</center>
 <hr>

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 Human [http://en.wikipedia.org/wiki/Human_weight weights] and [http://en.wikipedia.org/wiki/Human_height heights] are known to be approximately Normally distributed. Look at the [[SOCR_Data_Dinov_020108_HeightsWeights |SOCR Weighs and Heights Dataset]] and use the [[SOCR_EduMaterials_Activities_Histogram_Graphs | 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 10<sup>th</sup> percentile (shortest 10% for women) in height for college women, then what is the largest height closest to hers?
+* 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 10<sup>th</sup> 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)?
 <center>[[Image:SOCR_EBook_Dinov_RV_Normal_013108_Fig14.jpg|500px]]</center>

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 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.
-* The back and forth linear transformations converting between Standard and General Normal Distributions are always useful in such analyses (Let ''X'' denotes General (<math>X\sim N(\mu,\sigma^2)</math>) and ''Z'' denotes Standard (<math>X\sim N(0,1)</math>) Normal random variables):
+* The back and forth linear transformations converting between Standard and General Normal Distributions are always useful in such analyses (Let ''X'' denotes General (<math>X\sim N(\mu,\sigma^2)</math>) and ''Z'' denotes Standard (<math>Z\sim N(0,1)</math>) Normal random variables):
 : <math>Z = {X-\mu \over \sigma}</math> converts general normal scores to standard (Z) values.
-: <math>X = \mu +Z\sigma</math> converts standard scores to general normal values.
+: <math>X = \mu +Z\sigma \ </math> converts standard scores to general normal values.
 ===Examples===

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-==[[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)===
-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.
+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.
-* The back and forth linear transformations converting between Standard and General Normal distributions are always useful in such analyses (Let ''X'' denotes General (<math>X\sim N(\mu,\sigma^2)</math>) and ''Z'' denotes Standard (<math>X\sim N(0,1)</math>) Normal random variables):
+* The back and forth linear transformations converting between Standard and General Normal Distributions are always useful in such analyses (Let ''X'' denotes General (<math>X\sim N(\mu,\sigma^2)</math>) and ''Z'' denotes Standard (<math>X\sim N(0,1)</math>) Normal random variables):
 : <math>Z = {X-\mu \over \sigma}</math> converts general normal scores to standard (Z) values.
 : <math>X = \mu +Z\sigma</math> converts standard scores to general normal values.
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 ====[[SOCR_EduMaterials_Activities_Normal_Probability_examples | A large number of Normal distribution examples using SOCR tools is available here]]====
-====Textbook prices====
+====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 guarantee she spends only as much as 30% of the population? (<math>P(X<184.512)=0.3</math>)
 <center>[[Image:SOCR_EBook_Dinov_RV_Normal_013108_Fig12.jpg|500px]]</center>
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 ===References===
-* [[SOCR_EduMaterials_Activities_Histogram_Graphs | Histogram plots]]
+* [[SOCR_EduMaterials_Activities_Histogram_Graphs | Histogram Plots]]
-* [[SOCR_EduMaterials_Activities_BoxPlot | Box-and-whisker plots]]
+* [[SOCR_EduMaterials_Activities_BoxPlot | Box-and-whisker Plots]]
 * [[SOCR_EduMaterials_Activities_DotChart |Dotplot]]
-* [[SOCR_EduMaterials_Activities_QQChart |Quantile-Quantile probability plot]]
+* [[SOCR_EduMaterials_Activities_QQChart |Quantile-Quantile Probability Plot]]
 * [http://socr.ucla.edu/Applets.dir/Normal_T_Chi2_F_Tables.htm SOCR High-Precision Normal Distribution Calculator]