document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1116239>Question 1116239</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A market gardener in Tonga sells cabbages to a supermarket. She claims that the weights of the cabbages have a normal distribution with a mean weight of 1200 grams and a standard deviation of 50 grams.\r<BR>\n" );
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document.write( "(i) A cabbage is chosen at random, calculate the probability that its recorded weight is less than 1190 grams.\r<BR>\n" );
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document.write( "(ii) A consumer officer for the supermarket checks the gardener’s claim by weighing 40 of the cabbages. If the market gardener’s claim is true, calculate the probability that the 40 cabbages have a mean weight of less than 1190 grams. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #731304 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=731304\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> z=(x-mean)/sd<BR>\n" );
document.write( "=(1190-1200)/50<BR>\n" );
document.write( "=-.2  <BR>\n" );
document.write( "Probability z< -.2 is 0.4207<BR>\n" );
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document.write( "for 40 cabbages the denominator is sd/sqrt(n)<BR>\n" );
document.write( "z=(-10)/50/sqrt(40)<BR>\n" );
document.write( "=-10*sqrt(40)/50=-1.26<BR>\n" );
document.write( "Probability z < -1.26 is 0.1038<BR>\n" );
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