document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1031227>Question 1031227</A>: <I><SPAN STYLE=\"word-break: break-all;\"> At a fast Food restaurant, the expected number of customers who will spend at least $10 during the lunchtime period from 12:00 noon to 2:00 P.M is 221 and the variance is 33.15. Assume this is a binomial model. Determine the number of customers will be in this fast food restaurant on this Friday during the lunch time period from 12:00 noon to 2:00P.M.\r<BR>\n" );
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document.write( "I am completely lost here, is there enough info to solve the problem? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #645980 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=645980\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given information:<BR>\n" );
document.write( "Expected value E is E = 221<BR>\n" );
document.write( "Variance V is V = 33.15\r<BR>\n" );
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document.write( "We'll use the formulas<BR>\n" );
document.write( "E = n*p<BR>\n" );
document.write( "V = n*p*(1-p)<BR>\n" );
document.write( "which are the formulas for the expected value and variance of a binomial distribution<BR>\n" );
document.write( "n is the sample size<BR>\n" );
document.write( "p is the probability of success<BR>\n" );
document.write( "The ultimate goal is to find the value of n\r<BR>\n" );
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document.write( "Expected Value:<BR>\n" );
document.write( "E = n*p<BR>\n" );
document.write( "221 = n*p ... plug in the given expected value<BR>\n" );
document.write( "n*p = 221\r<BR>\n" );
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document.write( "Variance:<BR>\n" );
document.write( "V = n*p*(1-p)<BR>\n" );
document.write( "V = 221*(1-p) ... plug in n*p = 221<BR>\n" );
document.write( "33.15 = 221*(1-p) ... plug in the given variance\r<BR>\n" );
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document.write( "Now we solve for p<BR>\n" );
document.write( "33.15 = 221*(1-p)<BR>\n" );
document.write( "33.15 = 221-221p<BR>\n" );
document.write( "33.15-221 = -221p<BR>\n" );
document.write( "-187.85 = -221p<BR>\n" );
document.write( "-221p = -187.85<BR>\n" );
document.write( "p = -187.85/(-221)<BR>\n" );
document.write( "p = 0.85\r<BR>\n" );
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document.write( "The probability of success is 0.85<BR>\n" );
document.write( "This means the probability of picking one person who spent at least $10 is 0.85\r<BR>\n" );
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document.write( "Use p = 0.85 to find n\r<BR>\n" );
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document.write( "n*p = 221<BR>\n" );
document.write( "n*0.85 = 221 ... plug in p = 0.85<BR>\n" );
document.write( "n = 221/0.85<BR>\n" );
document.write( "n = 260\r<BR>\n" );
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document.write( "So there are 260 people in the sample\r<BR>\n" );
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document.write( "--------------------------------------------------------\r<BR>\n" );
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document.write( "Final Answer: <font size=5 color = red>260</font><BR>\n" );
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