document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1202307>Question 1202307</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A popular soft drink is sold in 2.5-litre (i.e., 2,500 millilitres) bottles. Due to variations in <BR>\n" );
document.write( "the production process, bottles have a mean of 2,500 millilitres and a standard deviation of <BR>\n" );
document.write( "22, normally distributed.<BR>\n" );
document.write( "(a) If the process fills bottles by more than 25 millilitres, the overflow will cause the machine <BR>\n" );
document.write( "to overflow. What is the probability of this occurring?<BR>\n" );
document.write( "(b) What is the probability of underfilling bottles by at least 15 millilitres? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #837037 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=837037\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> mean is 2500.<BR>\n" );
document.write( "standard deviation is 22.\r<BR>\n" );
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document.write( "(a) If the process fills bottles by more than 25 millilitres, the overflow will cause the machine<BR>\n" );
document.write( "to overflow. What is the probability of this occurring?\r<BR>\n" );
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document.write( "i think what the probllem is saying is that the overflow will occur when the bottle is filled to more than 2525 millilitres.<BR>\n" );
document.write( "that would be 25 millilitres more than the mean of 2500.<BR>\n" );
document.write( "the z-score woulld be equal to (2525 - 2500) / 22 = 25 / 22 = 1.136363636.<BR>\n" );
document.write( "the probability of that occurring would be equal to .1279022539.<BR>\n" );
document.write( "that's the areaa to the right of that z-score.<BR>\n" );
document.write( "that means that the probability of getting a z-score greater than that is 1.126363636.\r<BR>\n" );
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document.write( "(b) What is the probability of underfilling bottles by at least 15 millilitres?\r<BR>\n" );
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document.write( "the z-score would be equal to (2485 - 2500) / 22 = -15 / 22 = -.6818181818.<BR>\n" );
document.write( "the probbility of that occurring would be equal to .2476768904.<BR>\n" );
document.write( "that's the area to the left of that z-score.<BR>\n" );
document.write( "that means that the probability of getting a z-score less than that is .2476768904.\r<BR>\n" );
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document.write( "the calculator at <  rel=nofollow HREF= \"https://www.hackmath.net/en/calculator/normal-distribution\" target = \"_blank\">https://www.hackmath.net/en/calculator/normal-distribution</a> can be used to verify these results.\r<BR>\n" );
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document.write( "here are the results from this  calculator.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2023/051601.jpg\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2023/051602.jpg\">\r<BR>\n" );
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document.write( "the calculator can be used with z-scores or raw scores.<BR>\n" );
document.write( "if z-scores, the mean is 0 and the standard deviation is 1.<BR>\n" );
document.write( "otherwise, use the mean and standard deviation given.<BR>\n" );
document.write( " </SPAN>\n" );
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