正态分布到标准正态分布的转换
2015-03-29 10:11
本GeoGebra范例演示了如何将一般正态分布转换为标准正态分布。通过交互式滑块调整均值和标准差,用户可以直观地观察正态分布曲线与标准正态分布曲线之间的关系。范例利用积分命令计算特定区间内的概率,并展示了对应的Z值及概率文本说明,帮助学习者深入理解正态分布的标准化过程及其在概率统计中的应用。
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.639.0" app="classic" platform="w" id="e6a1063d-93f7-48cd-81a7-febec3e4f94c" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/apps/xsd/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="1745" height="885" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.12893982808022922" orientation="1" />
<pane location="1" divider="0.5706214689265536" orientation="0" />
</panes>
<views>
<view id="512" toolbar="0 | 1 501 5 19 , 67 | 2 15 45 18 , 7 37 | 514 3 9 , 13 44 , 47 | 16 | 551 550 11 , 22 , 23 , 55 56 57 , 12 | 69 | 510 511 , 512 513 | 533 531 , 534 532 , 522 523 , 537 536 , 535 | 521 520 | 36 , 38 49 560 | 571 30 29 570 31 33 | 17 | 540 40 41 42 , 27 28 35 , 6 , 502" visible="false" inframe="false" stylebar="false" location="1,1,1" size="500" window="100,100,600,400" />
<view id="1" visible="true" inframe="false" stylebar="true" location="1,0" size="505" window="100,100,600,400" />
<view id="4" toolbar="0 || 2020 , 2021 , 2022 , 66 || 2001 , 2003 , 2002 , 2004 , 2005 || 2040 , 2041 , 2042 , 2044 , 2043" visible="false" inframe="false" stylebar="true" location="1,1" size="300" window="100,100,600,400" />
<view id="8" toolbar="1001 | 1002 | 1003 || 1005 | 1004 || 1006 | 1007 | 1010 || 1008 1009 || 66 68 || 6" visible="false" inframe="false" stylebar="false" location="1,3" size="300" window="100,100,600,400" />
<view id="16" visible="true" inframe="false" stylebar="true" location="1,2" size="319" window="50,50,500,500" />
<view id="2" visible="true" inframe="false" stylebar="false" location="3" size="225" tab="ALGEBRA" window="100,100,250,400" />
<view id="32" visible="false" inframe="false" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="64" toolbar="0" visible="false" inframe="false" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="128" visible="false" inframe="false" stylebar="false" location="1" size="480" window="50,50,500,500" />
<view id="4097" visible="false" inframe="false" stylebar="true" location="1" size="392" window="433,176,700,550" />
<view id="70" toolbar="0 || 2020 || 2021 || 2022" visible="false" inframe="false" stylebar="true" location="1" size="150" window="50,50,500,500" />
</views>
<toolbar show="true" items="0 39 | 1 501 67 , 5 19 , 72 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 | 16 51 64 , 70 | 10 34 53 11 , 24 20 22 , 21 23 | 55 56 57 , 12 | 36 46 , 38 49 50 , 71 | 30 29 54 32 31 33 | 17 26 62 73 , 14 68 | 25 52 60 61 | 40 41 42 , 27 28 35 , 6" position="1" help="false" />
<input show="true" cmd="true" top="algebra" />
<dockBar show="false" east="false" />
</perspective>
</perspectives>
<labelingStyle val="2"/>
<font size="16"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="1511" height="504"/>
<coordSystem xZero="728.0745536186671" yZero="404.4272795459611" scale="9.39162532723566" yscale="844.2727954596098"/>
<evSettings axes="true" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="26" gridType="0"/>
<bgColor r="255" g="255" b="255"/>
<axesColor r="0" g="0" b="0"/>
<gridColor r="192" g="192" b="192"/>
<lineStyle axes="1" grid="10"/>
<axis id="0" show="true" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="true" label="" unitLabel="" tickStyle="1" showNumbers="true" positiveAxis="true"/>
</euclidianView>
<euclidianView>
<viewNumber viewNo="2"/>
<size width="1511" height="318"/>
<coordSystem xZero="727.5307969865107" yZero="206.98148509339882" scale="173.87118249911646" yscale="161.2201323269465"/>
<evSettings axes="true" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="26" gridType="0"/>
<bgColor r="255" g="255" b="255"/>
<axesColor r="0" g="0" b="0"/>
<gridColor r="192" g="192" b="192"/>
<lineStyle axes="1" grid="10"/>
<axis id="0" show="true" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="true" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
</euclidianView>
<algebraView>
<mode val="1"/>
<collapsed val="5"/>
</algebraView>
<kernel>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<angleUnit val="degree"/>
<algebraStyle val="0" spreadsheet="0"/>
<coordStyle val="0"/>
</kernel>
<tableview min="-2" max="2" step="1"/>
<scripting blocked="false" disabled="false"/>
<construction title="Normal Distribution to Standard Normal Distribution" author="" date="">
<worksheetText above="." below="."/>
<element type="numeric" label="m">
<value val="-24"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="-50" max="50" absoluteScreenLocation="true" width="80" x="33" y="38" fixed="true" horizontal="true" showAlgebra="false"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<element type="numeric" label="SD">
<value val="2.34"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelOffset x="-6" y="48"/>
<labelMode val="1"/>
<slider min="0.1" max="20" absoluteScreenLocation="true" width="80" x="34" y="72" fixed="true" horizontal="true" showAlgebra="false"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="0.01" speed="1" type="0" playing="false"/>
</element>
<command name="Normal">
<input a0="m" a1="SD" a2="x" a3="false"/>
<output a0="f"/>
</command>
<element type="function" label="f">
<show object="true" label="false"/>
<objColor r="204" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="7" type="0" typeHidden="1"/>
<casMap>
<entry key="Integral[ℯ^((-(x - m)^2.00000000000000) / (SD^2.00000000000000 * 2.00000000000000)) / (abs(SD) sqrt(2.00000000000000π)),x]" val="((-1 / 2 * SD^(2)) * erf((((-sqrt(2)) * SD) * ((((-1 / 2 * m) * 2) * SD^(2) / SD^(2)) + x) / ((2 * SD^(2))))) / ((SD * abs(SD)))) + arbconst(133 + 56406)"/>
</casMap>
</element>
<command name="Point">
<input a0="xAxis"/>
<output a0="A"/>
</command>
<element type="point" label="A">
<show object="true" label="false"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="-20.87759538810093" y="0" z="1"/>
<pointSize val="7"/>
<pointStyle val="2"/>
</element>
<expression label="B" exp="(x(A), f(x(A)))" type="point" />
<element type="point" label="B">
<show object="false" label="false"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-20.87759538810093" y="0.06999377085441183" z="1"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="B" a1="A"/>
<output a0="a"/>
</command>
<element type="segment" label="a">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.06999377085441183" y="0" z="1.4613016275858617"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Integral">
<input a0="f" a1="-Infinity" a2="x(A)"/>
<output a0="b"/>
</command>
<element type="numeric" label="b">
<value val="0.9089572035438"/>
<show object="false" label="false"/>
<objColor r="255" g="0" b="0" alpha="0.4"/>
<layer val="0"/>
<labelMode val="2"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
</element>
<expression label="text1" exp=""Probability=" + (LaTeX[b]) + """ />
<element type="text" label="text1">
<show object="false" label="false"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.4" size="7" style="0"/>
<absoluteScreenLocation x="228" y="20"/>
</element>
<expression label="xN" exp="(x(A) - m) / SD" />
<element type="numeric" label="xN">
<value val="1.3343609452560135"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<command name="Normal">
<input a0="0" a1="1" a2="x" a3="false"/>
<output a0="g"/>
</command>
<element type="function" label="g">
<show object="true" label="false" ev="3"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<casMap>
<entry key="Integral[ℯ^((-(x - 0)^2.00000000000000) / (1^2.00000000000000 * 2.00000000000000)) / (abs(1) sqrt(2.00000000000000π)),x]" val="(1 / 2 * erf(((1 / 2 * sqrt(2)) * x))) + arbconst(4 + 978)"/>
</casMap>
</element>
<expression label="C" exp="(xN, 0)" type="point" />
<element type="point" label="C">
<show object="true" label="false" ev="3"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1.3343609452560135" y="0" z="1"/>
<pointSize val="5"/>
<pointStyle val="2"/>
</element>
<expression label="D" exp="(x(C), g(x(C)))" type="point" />
<element type="point" label="D">
<show object="false" label="false" ev="3"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1.3343609452560135" y="0.16378542379932368" z="1"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="C" a1="D"/>
<output a0="c"/>
</command>
<element type="segment" label="c">
<show object="true" label="false" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-0.16378542379932368" y="0" z="0.2185488729200223"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Integral">
<input a0="g" a1="-Infinity" a2="x(C)"/>
<output a0="d"/>
</command>
<element type="numeric" label="d">
<value val="0.9089572035438"/>
<show object="false" label="true" ev="3"/>
<objColor r="0" g="255" b="0" alpha="0.5"/>
<layer val="0"/>
<labelMode val="2"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
</element>
<expression label="text2" exp=""Probability=" + (LaTeX[d]) + """ />
<element type="text" label="text2">
<show object="false" label="false" ev="3"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.4" size="7" style="0"/>
<startPoint x="-1.6537001293355325" y="1.1597899244630911" z="1"/>
</element>
<expression label="xA" exp="x(A)" />
<element type="numeric" label="xA">
<value val="-20.87759538810093"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<expression label="zVal" exp="x(C)" />
<element type="numeric" label="zVal">
<value val="1.3343609452560135"/>
<objColor r="99" g="219" b="219" alpha="0.5"/>
</element>
<expression label="text3" exp=""z=\frac{x-" + (LaTeX[m]) + "}{" + (LaTeX[SD]) + "}=\frac{" + (LaTeX[xA]) + "- " + (LaTeX[m]) + "}{ " + (LaTeX[SD]) + "}=" + (LaTeX[zVal]) + """ />
<element type="text" label="text3">
<show object="true" label="false" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
<startPoint x="0.22125117262421945" y="1.1783980223271728" z="1"/>
</element>
<expression label="text4" exp=""z""/>
<element type="text" label="text4">
<show object="true" label="false" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.4" size="7" style="1"/>
<startPoint exp="C"/>
<labelOffset x="-2" y="-27"/>
</element>
<expression label="text5" exp=""x""/>
<element type="text" label="text5">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.4" size="7" style="1"/>
<startPoint exp="A"/>
<labelOffset x="14" y="-33"/>
</element>
</construction>
</geogebra>