document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1185732>Question 1185732</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The lengths of pregnancies in a small rural village are normally distributed with a mean of 270 days and a standard deviation of 17 days.\r<BR>\n" );
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document.write( "In what range would you expect to find the middle 95% of most pregnancies?<BR>\n" );
document.write( "Between ? and ?\r<BR>\n" );
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document.write( "If you were to draw samples of size 30 from this population, in what range would you expect to find the middle 95% of most averages for the lengths of pregnancies in the sample?<BR>\n" );
document.write( "Between ? and ?\r<BR>\n" );
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document.write( "Enter your answers as numbers. Your answers should be accurate to 1 decimal places. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #849619 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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/cgi-bin/show-face.mpl?user=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=849619\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to calculate the ranges:\r<BR>\n" );
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document.write( "**1. Middle 95% of Individual Pregnancies:**\r<BR>\n" );
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document.write( "*   For a normal distribution, the middle 95% falls within approximately 1.96 standard deviations of the mean.<BR>\n" );
document.write( "*   Lower bound: Mean - (1.96 * Standard Deviation) = 270 - (1.96 * 17) = 270 - 33.32 ≈ 236.7<BR>\n" );
document.write( "*   Upper bound: Mean + (1.96 * Standard Deviation) = 270 + (1.96 * 17) = 270 + 33.32 ≈ 303.3\r<BR>\n" );
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document.write( "So, you'd expect to find the middle 95% of pregnancies between approximately **236.7** and **303.3** days.\r<BR>\n" );
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document.write( "**2. Middle 95% of Sample Means (n = 30):**\r<BR>\n" );
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document.write( "When working with sample means, we use the standard error of the mean (SEM) instead of the population standard deviation. The SEM is calculated as:\r<BR>\n" );
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document.write( "SEM = Standard Deviation / √Sample Size = 17 / √30 ≈ 17 / 5.48 ≈ 3.1\r<BR>\n" );
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document.write( "*   Lower bound: Mean - (1.96 * SEM) = 270 - (1.96 * 3.1) = 270 - 6.076 ≈ 263.9<BR>\n" );
document.write( "*   Upper bound: Mean + (1.96 * SEM) = 270 + (1.96 * 3.1) = 270 + 6.076 ≈ 276.1\r<BR>\n" );
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document.write( "So, you'd expect to find the middle 95% of sample means for pregnancies (with samples of size 30) between approximately **263.9** and **276.1** days.<BR>\n" );
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