document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1162961>Question 1162961</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A manufacturer makes chocolate bars with a mean weight<BR>\n" );
document.write( "of 110 grams and a standard deviation of 2 grams. The<BR>\n" );
document.write( "weights are normally distributed.<BR>\n" );
document.write( "(a) What proportion of the bars is likely to be less in<BR>\n" );
document.write( "weight than 106 grams?<BR>\n" );
document.write( "(b) The manufacturer decides to make “bigger bars” with<BR>\n" );
document.write( "the same standard deviation as before. It is decided<BR>\n" );
document.write( "that the covers of these bigger bars will be marked<BR>\n" );
document.write( "‘minimum weight 115 grams’. What mean weight will<BR>\n" );
document.write( "have to be aimed if no more than one bar in 100 is to<BR>\n" );
document.write( "be less than 115 grams in weight? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #786933 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=786933\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> to answer question A, do the following:<BR>\n" );
document.write( "mean = 110<BR>\n" );
document.write( "standard deviation = 2<BR>\n" );
document.write( "use the following online calculator:<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://homepage.divms.uiowa.edu/~mbognar/applets/normal.html\" target = \"_blank\">https://homepage.divms.uiowa.edu/~mbognar/applets/normal.html</a><BR>\n" );
document.write( "your inputs will be:<BR>\n" );
document.write( "mean = 110<BR>\n" );
document.write( "standard deviation = 2<BR>\n" );
document.write( "x = 106<BR>\n" );
document.write( "select p(X < x) and hit the return.<BR>\n" );
document.write( "the calculator then tells you that the probability of getting a chocolate bar with a weight less than 106 grams is equal to .02275.<BR>\n" );
document.write( "here's what it looks like:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2020/073001.jpg\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "to answer question B, do the following.<BR>\n" );
document.write( "set the mean equal to 0 and the standard deviation equal to 1<BR>\n" );
document.write( "set p(X < x) to .01<BR>\n" );
document.write( "hit the return and the calculator tells you that the x is equal to -2.32635.<BR>\n" );
document.write( "that's the z-score that will have an area to the left of it equal to .01<BR>\n" );
document.write( "here's what it looks like.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2020/073002.jpg\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "use the z-score formula of z = (x - m) / s<BR>\n" );
document.write( "set z = -2.32635.<BR>\n" );
document.write( "set x = 115<BR>\n" );
document.write( "set s = 2<BR>\n" );
document.write( "the z-score formula becomes -2.32635 = (115 - m) / 2<BR>\n" );
document.write( "multiply both sides of this equation by 2 to get -2.32635 * 2 = 115 - m<BR>\n" );
document.write( "subtract 115 from both sides of this equation to get -2.32635 * 2 - 115 = -m<BR>\n" );
document.write( "simplify to get -119.6527 = -m<BR>\n" );
document.write( "multiply both sides of the equation by -1 to get:<BR>\n" );
document.write( "119.6527 = m<BR>\n" );
document.write( "that's your mean.<BR>\n" );
document.write( "confirm by using the calculator again.<BR>\n" );
document.write( "inputs will be:<BR>\n" );
document.write( "mean = 119.6527<BR>\n" );
document.write( "standard deviation = 2<BR>\n" );
document.write( "select p(X < x)<BR>\n" );
document.write( "x = 115<BR>\n" );
document.write( "hit the return and the calculator tells you that p(X < x) = .01<BR>\n" );
document.write( "here's what it looks like.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2020/073003.jpg\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this means that the probability of getting a chocolate weighing less than 115 grams when the mean is 119.6527 grams and the standard deviation is 2 grams is equal to .01.<BR>\n" );
document.write( ".01 is the same as 1/100.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "i'll be available to answer anyquestions you might have in regard to this.<BR>\n" );
document.write( "you could solve it by using the z-score table, but there's no necessity to do so unless you are told you can't use an online calculcor to solve it.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );