document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1103809>Question 1103809</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The amount of fill (weight of contents) put into a glass jar of spaghetti sauce is normally distributed with mean &#956; = 848 grams and standard deviation of &#963; = 15 grams.<BR>\n" );
document.write( "(a) Describe the distribution of x, the amount of fill per jar.<BR>\n" );
document.write( "skewed right<BR>\n" );
document.write( "normal    <BR>\n" );
document.write( "skewed left<BR>\n" );
document.write( "chi-square\r<BR>\n" );
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document.write( "(b) Find the probability that one jar selected at random contains between 842 and 863 grams. (Give your answer correct to four decimal places.) <BR>\n" );
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document.write( "(c) Describe the distribution of x, the mean weight for a sample of 27 such jars of sauce.<BR>\n" );
document.write( "skewed right<BR>\n" );
document.write( "normal    <BR>\n" );
document.write( "skewed left<BR>\n" );
document.write( "chi-square\r<BR>\n" );
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document.write( "(d) Find the mean of the x distribution. (Give your answer correct to the nearest whole number.) <BR>\n" );
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document.write( "(ii) Find the standard error of the x distribution. (Give your answer correct to two decimal places.) <BR>\n" );
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document.write( "(e) Find the probability that a random sample of 27 jars has a mean weight between 842 and 863 grams. (Give your answer correct to four decimal places.) <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #718501 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=718501\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is presumably normally distributed.<BR>\n" );
document.write( "z=(x-mean)/sd=(842-848)/15=-6/15=-0.4<BR>\n" );
document.write( "z=(863-848)/15=+1<BR>\n" );
document.write( "probability of z between those two numbers is 0.4968<BR>\n" );
document.write( "==================<BR>\n" );
document.write( "The next part is normally distributed (at least no reason given to suggest it isn't).<BR>\n" );
document.write( "Mean is 848<BR>\n" );
document.write( "The z values have the sd modified to be s/(sqrt(27)=2.89<BR>\n" );
document.write( "Therefore, the z values will be between -6/2.89=-2.08 and 15/2.89=5.19<BR>\n" );
document.write( "That probability is now 0.9812. </SPAN>\n" );
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