document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199053>Question 1199053</A>: <I><SPAN STYLE=\"word-break: break-all;\"> While this question was answered, it wasn't helpful for me. <BR>\n" );
document.write( "Q.The volumes of apple juice in cartons are normally distributed with a standard deviation of 120 mL. Find the mean, to the nearest whole number, if 34% of these cartons contain less that 961 mL of juice\r<BR>\n" );
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document.write( "A: I thought that 0.34 could be the probability of 'success' but I'm not sure of it or of where to go for this question. Much appreciated. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #832803 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=832803\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 34% is the probability that the cartons contain less than 961 ml of juice.<BR>\n" );
document.write( "that is also the area to the left of of the z-score represented by that value.\r<BR>\n" );
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document.write( "the z-score formula is z = (x - m) / s<BR>\n" );
document.write( "z is the z-score<BR>\n" );
document.write( "x is the raw score<BR>\n" );
document.write( "m is the mean<BR>\n" );
document.write( "s is the standard deviation\r<BR>\n" );
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document.write( "the z-score that has .34 of the area to the left of it is equal to -.412463135, according to the online calculator at <a  rel=nofollow HREF= \"https://davidmlane.com/hyperstat/z_table.html\" target = \"_blalnk\">https://davidmlane.com/hyperstat/z_table.html</a>\r<BR>\n" );
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document.write( "this is what the results of that calculator look like:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2022/120901.jpg\">\r<BR>\n" );
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document.write( "since you are working with the z-score, the mean is made equal to 0 and the standard deviation is made equal to 1.\r<BR>\n" );
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document.write( "the z-score that has .34 of the area under the normal distribution curve is equal to -.412, according to that calculator.\r<BR>\n" );
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document.write( "to find the mean, you would use the z-score formula.\r<BR>\n" );
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document.write( "in this problem, that formula becomes:<BR>\n" );
document.write( "-.412 = (961 - m) / 120<BR>\n" );
document.write( "-.412 is the z-score<BR>\n" );
document.write( "961 is the raw score]<BR>\n" );
document.write( "m is the mean<BR>\n" );
document.write( "120 is the standard deviation.\r<BR>\n" );
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document.write( "multiply both sides of that formul by 120 to get:<BR>\n" );
document.write( "-.412 * 120 = 961 - m<BR>\n" );
document.write( "add m to both sides of that equation and add .412 * 120 to both sides of that equation to get:<BR>\n" );
document.write( "m = 961 + .412 * 120<BR>\n" );
document.write( "solve for m to get m = 1010.44<BR>\n" );
document.write( "that's your mean.<BR>\n" );
document.write( "round to the nearest integer to get 1010.\r<BR>\n" );
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document.write( "here's what it looks like on that calculator.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2022/120901.jpg\">\r<BR>\n" );
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document.write( "since you are working with the raw score, the mean is made 1010.44 and the standard deviation is made 120.\r<BR>\n" );
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document.write( "let me know if you have any questions.<BR>\n" );
document.write( "theo\r<BR>\n" );
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document.write( " </SPAN>\n" );
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