document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1179340>Question 1179340</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the paid-up life insurance value of a $50,000 20-year limited-payment life insurance policy that has been owned for 10 years, if the value per $1,000 unit is $428? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850244 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=850244\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You've got the correct approach! Here's a recap of the steps and the final answer:\r<BR>\n" );
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document.write( "1. Define the Variables:\r<BR>\n" );
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document.write( "Mean (μ) = 287 grams<BR>\n" );
document.write( "Standard deviation (σ) = 19 grams<BR>\n" );
document.write( "Lower bound (x1) = 251 grams<BR>\n" );
document.write( "Upper bound (x2) = 346 grams<BR>\n" );
document.write( "2. Calculate the Z-Scores:\r<BR>\n" );
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document.write( "We need to convert the given weights to z-scores 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( "For x1 = 251 grams:<BR>\n" );
document.write( "z1 = (251 - 287) / 19 = -36 / 19 ≈ -1.89<BR>\n" );
document.write( "For x2 = 346 grams:<BR>\n" );
document.write( "z2 = (346 - 287) / 19 = 59 / 19 ≈ 3.11<BR>\n" );
document.write( "3. Find the Probabilities:\r<BR>\n" );
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document.write( "We want to find the probability P(-1.89 < Z < 3.11). This is equal to P(Z < 3.11) - P(Z < -1.89).\r<BR>\n" );
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document.write( "Using a z-table or calculator:<BR>\n" );
document.write( "P(Z < 3.11) ≈ 0.9991<BR>\n" );
document.write( "P(Z < -1.89) ≈ 0.0294<BR>\n" );
document.write( "4. Calculate the Probability:\r<BR>\n" );
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document.write( "P(-1.89 < Z < 3.11) = 0.9991 - 0.0294 ≈ 0.9697<BR>\n" );
document.write( "5. Convert to Percentage:\r<BR>\n" );
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document.write( "0.9697 * 100% = 96.97%<BR>\n" );
document.write( "Answer:\r<BR>\n" );
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document.write( "The probability that a randomly picked fruit will weigh between 251 grams and 346 grams is approximately 96.97%. </SPAN>\n" );
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