document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1202329>Question 1202329</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If Z has a mean of 0 and a standard deviation of 1, determine the probability,\r<BR>\n" );
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document.write( "P(|Z| <2.0)\r<BR>\n" );
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document.write( "the answer is 0.9544 but i have no idea how they got that. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #837070 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=837070\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "You can use a stats calculator such as a TI84 <BR>\n" );
document.write( "<a  rel=nofollow HREF=\"https://www.statology.org/normal-probabilities-ti-84-calculator/\">https://www.statology.org/normal-probabilities-ti-84-calculator/</a><BR>\n" );
document.write( "or spreadsheet software<BR>\n" );
document.write( "<a  rel=nofollow HREF=\"https://www.statology.org/normalcdf-in-excel/\">https://www.statology.org/normalcdf-in-excel/</a><BR>\n" );
document.write( "or something like this<BR>\n" );
document.write( "<a  rel=nofollow HREF=\"https://davidmlane.com/normal.html\">https://davidmlane.com/normal.html</a>\r<BR>\n" );
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document.write( "However, I'll be using a table instead.<BR>\n" );
document.write( "This is the table I'll be using:<BR>\n" );
document.write( "<a  rel=nofollow HREF=\"https://www.ztable.net/\">https://www.ztable.net/</a><BR>\n" );
document.write( "A similar table is found in the back of any stats textbook.\r<BR>\n" );
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document.write( "Use that table to determine these two approximations:<BR>\n" );
document.write( "P(Z < -2.00) = 0.02275<BR>\n" );
document.write( "P(Z < 2.00) = 0.97725\r<BR>\n" );
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document.write( "Then we can compute the following.<BR>\n" );
document.write( "P(a < Z < b) = P(Z < b) - P(Z < a)<BR>\n" );
document.write( "P(-2 < Z < 2) = P(Z < 2) - P(Z < -2)<BR>\n" );
document.write( "P(-2 < Z < 2) = 0.97725 - 0.02275<BR>\n" );
document.write( "P(-2 < Z < 2) = 0.9545<BR>\n" );
document.write( "P(|Z| < 2) = 0.9545\r<BR>\n" );
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document.write( "This is the approximate area under the Z curve between z = -2 and z = 2<BR>\n" );
document.write( "The third link I mentioned at the top will draw out the diagram I'm describing. \r<BR>\n" );
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document.write( "The result 0.9545 is a bit off compared to 0.9544, but I think it's close enough. <BR>\n" );
document.write( "This slight discrepancy is due to rounding error.<BR>\n" );
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