document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1052805>Question 1052805</A>: <I><SPAN STYLE=\"word-break: break-all;\"> t is known that the average weight of a piece of easter candy is 65.2 grams with a standard deviation of 4 grams. assume distribution is normal.\r<BR>\n" );
document.write( "\n" );
document.write( "B.) The study guide wants me to find the probability that the average weight of 50 pieces is between 64 and 66 grams. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #668111 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=668111\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> mean = 65.2 grams<BR>\n" );
document.write( "standard deviation = 4 grams.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you want to find the probability that the average weight of 50 pieces is between 64 and 66 grams.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the sample size is 50.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the standard error is equal to the standard deviation divided by the square root of the sample size.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that makes the standard error equal to 4 / sqrt(50) = .5656854249.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "for practical purposes, this can be rounded to 4 decimal places.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the standard error is therefore calculated to be .5657.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you need to find the z-score for the lower threshold and the z-score for the higher threshold.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the formula for z-score is z = (x-m) / s\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\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 error in this case.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your two threshold z-scores will be calculated as follows.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "lower threshold z-score becomes z = (64 - 65.2) / .5657\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "higher threshold z-score becomes z = (66 - 65.2) / .5657\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "results are:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "lower threshold z-score = -2.121265689 which can be shortened to -2.12 for practical purposes, since that's the accuracy of most z-score tables.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "higher threshold z-score = 1.414177126 which can be shortened to 1.41 for practical purposes, since that's the accuracy of most z-score tables.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you would look these scores up in the z-score table and get the area to the left of that z-score for each one.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you would then subtract the smaller area from the larger area to get the area between.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the lower z-score gives an area to the left of it of .0170\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the higher z-score gives an area to the left of it of .9207\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the area in between is equal to .9207 minus .0170 which is equal to.9037\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that's your solution.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this can be visually represented as shown below:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2016/101401.jpg\" alt=\"$$$\" </>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the z-score table i used can be found here:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<a  rel=nofollow HREF= \"http://www.stat.ufl.edu/~athienit/Tables/Ztable.pdf\" target = \"_blank\">http://www.stat.ufl.edu/~athienit/Tables/Ztable.pdf</a>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the z-score calculator i used to give you the visual presentation can be found here:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<a  rel=nofollow HREF= \"http://davidmlane.com/hyperstat/z_table.html\" taerget = \"_blank\">http://davidmlane.com/hyperstat/z_table.html</a> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );