document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1150536>Question 1150536</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 4. A manufacturer fills jars with coffee. The weight of coffee, W grams, in a jar can be modelled by a normal distribution with mean 232 grams and standard deviation 5 grams.<BR>\n" );
document.write( "(i) Find P(W < 227)? [4 marks]<BR>\n" );
document.write( "(ii) One hundred jars of coffee are selected at random. Find the probability that more than 23 jars contains less than 227 grams of coffee. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #772357 by </B><A HREF=/tutors/aboutme.mpl?userid=Glaviolette><B>Glaviolette(140)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Glaviolette><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=Glaviolette><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=772357\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (i) z = (227-232)/5 = -1<BR>\n" );
document.write( "P(W < 227) = .1587 (from z-score table)\r<BR>\n" );
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document.write( "(ii) To determine the probability that more than 23 jars out of 100 weigh less than 227 grams, I would use a binomial distribution.  More than 23 weighing less than 227 is the same as 76 or less weighing more than 227.<BR>\n" );
document.write( "P(> 23 of 100 weigh less than 227) = P(< or = 76 weighing more than 227)<BR>\n" );
document.write( "= binomcdf(100, .8413, 76)<BR>\n" );
document.write( "= .0225\r<BR>\n" );
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document.write( "OR More than 23 weighing less than 227 is the complement of 23 or less weighing less than 227<BR>\n" );
document.write( "P(> 23 of 100 weigh less than 227) = 1 - P(< or = 23 less than 227)<BR>\n" );
document.write( "= 1 - .9774<BR>\n" );
document.write( "= .0225 </SPAN>\n" );
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