document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=909978>Question 909978</A>: <I><SPAN STYLE=\"word-break: break-all;\">  (i).The length of human pregnancies from conception to birth approximates a normal distribution with a mean of 266 days and a variance of 256 days. What proportion of all pregnancies will last between 240 days and 270 days (roughly between 8 and 9 months)? Draw a normal curve to illustrate your probability.\r<BR>\n" );
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document.write( "(ii). What length of time marks the shortest 70% of all pregnancies? Draw a normal curve to illustrate your probability. <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 #552168 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=552168\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (i).The length of human pregnancies from conception to birth approximates a normal distribution with a mean of 266 days and a variance of 256 days. What proportion of all pregnancies will last between 240 days and 270 days (roughly between 8 and 9 months)? Draw a normal curve to illustrate your probability.<BR>\n" );
document.write( "Draw a normal curve ; plot mean = 266 in the middle ; plot 240 to the left<BR>\n" );
document.write( "adn 270 to the right of the mean.<BR>\n" );
document.write( "z(240) = (240-266)/16 = -26/16 = -13/8<BR>\n" );
document.write( "z(270) = (270-266)/16 = 4/16 = 1/4<BR>\n" );
document.write( "P(240 < x < 270) = P(-13/8< z < 1/4) = normalcdf(-13/8,1/4) = 0.5466<BR>\n" );
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document.write( " (ii). What length of time marks the shortest 70% of all pregnancies? Draw a normal curve to illustrate your probability.<BR>\n" );
document.write( "Find the z-value with a left tail of 0.7<BR>\n" );
document.write( "invNorm(0.7) = 0.5244<BR>\n" );
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document.write( "Find the corresponding time value::<BR>\n" );
document.write( "x = z*s + u<BR>\n" );
document.write( "x = 0.5244*16 + 266 = 274.39 days<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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