document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1132735>Question 1132735</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Cans of regular soda have volumes with a mean of 12.63 oz and a standard deviation of 0.12 oz. Is it unusual for a can to contain 12.77 oz of​ soda?<BR>\n" );
document.write( "Minimum​ \"usual\" value =____oz </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #749963 by </B><A HREF=/tutors/aboutme.mpl?userid=Alex.33><B>Alex.33(110)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alex.33><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=Alex.33><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=749963\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 12.77 is (12.77-12.63)/0.12=(7/6) standard deviations away from the mean.<BR>\n" );
document.write( "I cannot be certain whether it is 'unusual', but by properties of the normal distribution, the possibility that the volume of a random can is within (7/6) STD is between 68.3%(within 1 STD from mean) and 95.4%(within 2 STD from the mean), closer to the former.<BR>\n" );
document.write( "You can then decide whether this is 'unusual' based on the definition of 'usual'.\r<BR>\n" );
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document.write( "But to show how to solve the problem fully I now assume 'within 2 STD from the mean' to be 'usual'. If this is different than the definition you've given, the problem can be solved similarly.<BR>\n" );
document.write( "Then the 12.77-oz soda is usual.<BR>\n" );
document.write( "The minimum 'usual' value, under this definition, is 12.63-2*.12=12.39 oz.\r<BR>\n" );
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