document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1169956>Question 1169956</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A Food Marketing Institute found that 30% of households spend more than $125 a week on groceries. Assume the population proportion is 0.3 and a simple random sample of 86 households is selected from the population. What is the probability that the sample proportion of households spending more than $125 a week is between 0.37 and 0.49?\r<BR>\n" );
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document.write( "Note: You should carefully round any z-values you calculate to 4 decimal places to match wamap's approach and calculations. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #794806 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=794806\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> z=(0.37-0.30)/sqrt(0.3*0.7/86)<BR>\n" );
document.write( "=0.07/0.0494=1.4166<BR>\n" );
document.write( "z=(0.49-0.30)/0.0494=3.8462<BR>\n" );
document.write( "probability z is between those two values is 0.0782\r<BR>\n" );
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document.write( "note, rounding to four decimal places in the above assumes the proportion given will be an integer. It is not, so that the proportion used is a rounding, and four decimal places is not going to be accurate even though it may be calculated. </SPAN>\n" );
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