document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206850>Question 1206850</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let z be a standard normal random variable with mean 𝜇 = 0 and standard deviation 𝜎 = 1. Use Table 3 in Appendix I to find the probability. (Round your answer to four decimal places.)<BR>\n" );
document.write( "P(z > 1.13) = <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #844526 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=844526\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Answer: <font color=red size=4>0.1292</font><BR>\n" );
document.write( "This value is approximate.\r<BR>\n" );
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document.write( "Explanation\r<BR>\n" );
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document.write( "As the instructions mention, turn to the page that has Table 3 in Appendix I.<BR>\n" );
document.write( "Locate the row that starts with 1.1<BR>\n" );
document.write( "Locate the column that has 0.03 at the top.<BR>\n" );
document.write( "The intersection of this row and column yields the approximate value 0.87076<BR>\n" );
document.write( "It indicates that P(Z < 1.13) = 0.87076 approximately.\r<BR>\n" );
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document.write( "For students following along that don't have their stats textbook with them, refer to online resources such as this<BR>\n" );
document.write( "<a  rel=nofollow HREF=\"https://www.ztable.net/\">https://www.ztable.net/</a>\r<BR>\n" );
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document.write( "Then,<BR>\n" );
document.write( "P(Z > 1.13) = 1-P(Z < 1.13)<BR>\n" );
document.write( "P(Z > 1.13) = 1-0.87076<BR>\n" );
document.write( "P(Z > 1.13) = 0.12924<BR>\n" );
document.write( "P(Z > 1.13) = <font color=red>0.1292</font> which is the final answer when rounding to 4 decimal places.\r<BR>\n" );
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document.write( "Verification\r<BR>\n" );
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document.write( "There are many ways to verify this with a handheld calculator, an app on your phone, or a website.<BR>\n" );
document.write( "Feel free to explore your favorite method. <BR>\n" );
document.write( "It's probably best to use a tool that is approved by your teacher for exam settings. <BR>\n" );
document.write( "Once you get outside of the classroom, you can of course choose any method you want.\r<BR>\n" );
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document.write( "On the TI84 is the command called <font color=red>NormalCDF</font> which is found by pressing the button labeled \"2nd\" and then pressing the VARS key.<BR>\n" );
document.write( "The command to type in would be <font color=red>NormalCDF(1.13,999)</font> where mu = 0 and sigma = 1 are the default options.<BR>\n" );
document.write( "The 999 is to represent some really large number effectively acting as \"infinity\" so to speak.\r<BR>\n" );
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document.write( "You can also use an online tool such as this<BR>\n" );
document.write( "<a  rel=nofollow HREF=\"https://davidmlane.com/normal.html\">https://davidmlane.com/normal.html</a><BR>\n" );
document.write( "Which is completely free and offers a more intuitive user interface. No need to memorize function commands or what inputs go where. <BR>\n" );
document.write( "As a bonus, it offers a really nice diagram as well. <BR>\n" );
document.write( "Notice this diagram has the curve entirely above the x axis. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=math_tutor2020&illustration_name=UploadedScreenshot_48.png\">\r<BR>\n" );
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document.write( "Whereas WolframAlpha has a flaw to it when offering a diagram.<BR>\n" );
document.write( "This is what shows up when you type in <font color=red>P(Z > 1.13)</font> and select the \"referring to statistics\" option.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=math_tutor2020&illustration_name=UploadedScreenshot_49.png\"><BR>\n" );
document.write( "Some parts of this curve are mistakenly below the x axis. That's not good. <BR>\n" );
document.write( "I'm not sure why WolframAlpha has this weird flaw. But it's something to keep in mind. <BR>\n" );
document.write( "Tutor @MathLover1 appears to have used this slightly faulty diagram. <BR>\n" );
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