document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1207570>Question 1207570</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The lengths of pregnancies in a small rural village are normally distributed with a mean of 266 days and a standard deviation of 17 days.\r<BR>\n" );
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document.write( "What percentage of pregnancies last beyond 252 days?<BR>\n" );
document.write( "P(X > 252 days) =  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #845519 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=845519\">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 specialized Z calculator as the other tutor mentions. <BR>\n" );
document.write( "I'll use a Z table.\r<BR>\n" );
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document.write( "First we need to compute the z score.<BR>\n" );
document.write( "z = (x - mu)/sigma<BR>\n" );
document.write( "z = (252 - 266)/17<BR>\n" );
document.write( "z = -0.82 approximately<BR>\n" );
document.write( "I'm rounding to two decimal places because it is standard for many Z tables.\r<BR>\n" );
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document.write( "Such tables can be found in the back of your stats textbook.<BR>\n" );
document.write( "If you don't have your textbook with you, then you can use an online resource 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( "Let me know if you have questions on how to read the table.\r<BR>\n" );
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document.write( "Using such a table will determine that<BR>\n" );
document.write( "P(Z < -0.82) = 0.20611<BR>\n" );
document.write( "and then that leads to this<BR>\n" );
document.write( "P(Z > -0.82) = 1-P(Z < -0.82)<BR>\n" );
document.write( "P(Z > -0.82) = 1-0.20611<BR>\n" );
document.write( "P(Z > -0.82) = 0.79389<BR>\n" );
document.write( "Each decimal value mentioned is approximate.\r<BR>\n" );
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document.write( "That translates back to P(X > 252) = 0.79389 approximately when the mean is mu = 266 and the standard deviation is sigma = 17.\r<BR>\n" );
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document.write( "The percentage of pregnancies that last beyond 252 days is <font color=red>approximately 79.389%</font> depending how you round it.\r<BR>\n" );
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document.write( "This accuracy can be improved through the use of a specialized Z calculator. <BR>\n" );
document.write( "Some teachers will allow specialized Z calculators; while other teachers will only allow a stats table and standard calculator.<BR>\n" );
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