document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1171440>Question 1171440</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The study about the height of Southeast Asian women follows a normal distribution with a mean of 153 cm and standard deviation 12 cm. What is the probability that a randomly selected woman’s height is less than 150 cm? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850931 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=850931\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's solve this problem using the properties of the normal distribution.\r<BR>\n" );
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document.write( "**1. Define the Variables**\r<BR>\n" );
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document.write( "* Mean (μ) = 153 cm<BR>\n" );
document.write( "* Standard deviation (σ) = 12 cm<BR>\n" );
document.write( "* We want to find the probability that a woman's height (X) is less than 150 cm, i.e., P(X < 150).\r<BR>\n" );
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document.write( "**2. Calculate the Z-score**\r<BR>\n" );
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document.write( "The Z-score represents how many standard deviations a value is from the mean. It's calculated using the formula:\r<BR>\n" );
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document.write( "* Z = (X - μ) / σ\r<BR>\n" );
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document.write( "In our case:\r<BR>\n" );
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document.write( "* Z = (150 - 153) / 12<BR>\n" );
document.write( "* Z = -3 / 12<BR>\n" );
document.write( "* Z = -0.25\r<BR>\n" );
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document.write( "**3. Find the Probability Using the Z-table or Calculator**\r<BR>\n" );
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document.write( "We need to find the probability P(Z < -0.25). This is the area under the standard normal distribution curve to the left of Z = -0.25.\r<BR>\n" );
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document.write( "You can find this probability using:\r<BR>\n" );
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document.write( "* A standard normal distribution table (Z-table)<BR>\n" );
document.write( "* A calculator with statistical functions<BR>\n" );
document.write( "* An online normal distribution calculator\r<BR>\n" );
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document.write( "Using a Z-table or calculator, you will find:\r<BR>\n" );
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document.write( "* P(Z < -0.25) ≈ 0.4013\r<BR>\n" );
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document.write( "**4. Interpret the Result**\r<BR>\n" );
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document.write( "The probability that a randomly selected Southeast Asian woman's height is less than 150 cm is approximately 0.4013, or 40.13%.\r<BR>\n" );
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document.write( "**Therefore, the probability is approximately 0.4013.**<BR>\n" );
document.write( " </SPAN>\n" );
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