document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205782>Question 1205782</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Each Filipino uses an average of 650 pounds of plastic in a year. Suppose that the distribution is approximately normal with a population standard deviation of 153.5 pounds. Assume the variable is normally distributed. Find the probability that a randomly selected Filipino uses \r<BR>\n" );
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document.write( "a.)	More than 800 pounds of paper in a year (10 points)\r<BR>\n" );
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document.write( "b.)	Less than 400 pounds a year (10 points)\r<BR>\n" );
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document.write( "c.)	Between 500 and 700 pounds a year (10 points)\r<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 #842876 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=842876\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> population mean is 650 and population standard deviation is 153.5.\r<BR>\n" );
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document.write( "z-score formula is z = (x-m)/s\r<BR>\n" );
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document.write( "in this problem:\r<BR>\n" );
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document.write( "x is the value of the randomly selected variable.<BR>\n" );
document.write( "m is the population mean<BR>\n" );
document.write( "s is the standard deviation.<BR>\n" );
document.write( "z is the z-score.\r<BR>\n" );
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document.write( "answers to your questions are shown below.\r<BR>\n" );
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document.write( "Find the probability that a randomly selected Filipino uses\r<BR>\n" );
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document.write( "a.) More than 800 pounds of paper in a year (10 points)\r<BR>\n" );
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document.write( "for x = 800, z = (800 - 650) / 153.5 = .9771986971.\r<BR>\n" );
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document.write( "area to the right of this z-score is equal to .1642.<BR>\n" );
document.write( "that's the probability that a random selected filipino uses more than 800 pounds of plastic in a year.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2024/012611.jpg\">\r<BR>\n" );
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document.write( "b.) Less than 400 pounds a year (10 points)\r<BR>\n" );
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document.write( "for x = 400, z = (400 - 650) / 153.5 = -1.628664495.\r<BR>\n" );
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document.write( "area to the left of this z-score is equal to .0517.<BR>\n" );
document.write( "that's the probability that a randomly selected filipino uses less than 400 pounds of plastic in a year.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2024/012612.jpg\">\r<BR>\n" );
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document.write( "c.) Between 500 and 700 pounds a year (10 points)\r<BR>\n" );
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document.write( "for x = 500, z = (500 - 650) / 153.5 = -.9771986971.<BR>\n" );
document.write( "for x = 700, z = (700 - 650) / 153.5 = .325732899.\r<BR>\n" );
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document.write( "area in between these two z-score is equal to .4635.<BR>\n" );
document.write( "that's the probability that a randomly selected filipino uses between 500 and 700 pounds of plastic in a year.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2024/012613.jpg\">\r<BR>\n" );
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document.write( "calculator used can be found at <a  rel=nofollow HREF= \"https://davidmlane.com/hyperstat/z_table.html\" target = \"_blank\">https://davidmlane.com/hyperstat/z_table.html</a>\r<BR>\n" );
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