document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1192325>Question 1192325</A>: <I><SPAN STYLE=\"word-break: break-all;\"> in a rice mill the bags of rice has mean weight of 5.05 kg and standard deviation is 0.02 kg. if a bag is selected at random then find the probability that its weight is below 5 kg? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #849043 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=849043\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **1. Understand the Problem**\r<BR>\n" );
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document.write( "* We're given a normal distribution of rice bag weights.<BR>\n" );
document.write( "* Mean weight (μ) = 5.05 kg<BR>\n" );
document.write( "* Standard deviation (σ) = 0.02 kg<BR>\n" );
document.write( "* We want to find the probability that a randomly selected bag weighs less than 5 kg.\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 tells us how many standard deviations a value is from the mean. <BR>\n" );
document.write( "* Formula: Z = (X - μ) / σ <BR>\n" );
document.write( "    * Where: <BR>\n" );
document.write( "        * X is the value we're interested in (5 kg)<BR>\n" );
document.write( "        * μ is the mean <BR>\n" );
document.write( "        * σ is the standard deviation\r<BR>\n" );
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document.write( "* Calculation: Z = (5 - 5.05) / 0.02 = -0.25\r<BR>\n" );
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document.write( "**3. Find the Probability**\r<BR>\n" );
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document.write( "* We need to find the area under the standard normal distribution curve to the left of Z = -0.25. <BR>\n" );
document.write( "* You can use:<BR>\n" );
document.write( "    * A Z-table: Look up the value corresponding to Z = -0.25 in a standard normal distribution table. <BR>\n" );
document.write( "    * Statistical software or calculator: Use functions like `norm.cdf()` in Python (scipy library) or similar functions in other tools.\r<BR>\n" );
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document.write( "* **Result:** The probability of a randomly selected bag weighing less than 5 kg is approximately **0.4013**.\r<BR>\n" );
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document.write( "**In summary:**\r<BR>\n" );
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document.write( "There's about a 40.13% chance that a randomly selected bag of rice from this mill will weigh less than 5 kg.<BR>\n" );
document.write( " </SPAN>\n" );
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