document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=476447>Question 476447</A>: <I><SPAN STYLE=\"word-break: break-all;\"> People end up tossing 12% of what they buy at the grocery store (Reader's Digest, March, 2009). Assume this is the true population proportion and that you plan to take a sample survey of 540 grocery shoppers to further investigate their behavior. \r<BR>\n" );
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document.write( "a.Show the sampling distribution of (p), the proportion of groceries thrown out by your sample respondents (to 4 decimals)?<BR>\n" );
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document.write( "b.What is the probability that your survey will provide a sample proportion within ±.03 of the population proportion (to 4 decimals)?<BR>\n" );
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document.write( "c.What is the probability that your survey will provide a sample proportion within ±.015 of the population proportion (to 4 decimals)? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #326748 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=326748\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a. the sampling distribution of proportions would be normally distributed, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N%28p%2C+sqrt%28%28pq%29%2Fn%29%29 ALIGN=MIDDLE  ALT=\"N%28p%2C+sqrt%28%28pq%29%2Fn%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or N(0.12,0.014).  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu+=+0.12 ALIGN=MIDDLE  ALT=\"mu+=+0.12\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sigma+=+0.014 ALIGN=MIDDLE  ALT=\"sigma+=+0.014\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "b. we want the probability under the standard normal table between <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+%28P+-+p%29%2Fsqrt%28%28pq%29%2Fn%29+=+0.03%2F0.014+=+2.14 ALIGN=MIDDLE  ALT=\"z+=+%28P+-+p%29%2Fsqrt%28%28pq%29%2Fn%29+=+0.03%2F0.014+=+2.14\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+%28P+-+p%29%2Fsqrt%28%28pq%29%2Fn%29+=+-0.03%2F0.014+=+-2.14 ALIGN=MIDDLE  ALT=\"z+=+%28P+-+p%29%2Fsqrt%28%28pq%29%2Fn%29+=+-0.03%2F0.014+=+-2.14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28-2.14+%3C+z+%3C+2.14%29+=+0.9838+-+0.0162+=+0.9676 ALIGN=MIDDLE  ALT=\"P%28-2.14+%3C+z+%3C+2.14%29+=+0.9838+-+0.0162+=+0.9676\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "c.  this follows the same procedure as in (b). </SPAN>\n" );
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