document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1034997>Question 1034997</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a convenience store makes over $200 approximately 75% of the days it is open. use the normal approximation to determine the probability that the store makes over $200 at least 265 out of 365 days. round your answer to the nearest thousandth. \r<BR>\n" );
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document.write( "I think the probability of success is (265/365) or (53/73) in simplist form and I also this the probability of failure is (100/365) or (20/73) in simplist form. I know we have to use this formula: \r<BR>\n" );
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document.write( "        P(at least r)= p ( r ) + p(r-1) + p( r-2) ....+p(0) <BR>\n" );
document.write( "And we use nCr P(success)^r * P(failure)^n-r <BR>\n" );
document.write( " But I don't understand what n or r is I  was thinking r equaled .75 but I am not sure.  <BR>\n" );
document.write( "I know the answer is .868 but I do not know how to get there. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #649729 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=649729\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> p = .75<BR>\n" );
document.write( "q = .25<BR>\n" );
document.write( "n = 365<BR>\n" );
document.write( "x = 265\r<BR>\n" );
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document.write( "mean = n*p = .75 * 365 = 273.75<BR>\n" );
document.write( "s = standard error of the mean = sqrt(n*p*q) = sqrt(365*.75*.25) = 8.272696054\r<BR>\n" );
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document.write( "adjust the value of x to account for discrete versus continuous by subtracting .5 from it.\r<BR>\n" );
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document.write( "x becomes 264.5\r<BR>\n" );
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document.write( "z = (x-m)/s = (24.5 - 273.75) / 8.272696054 = -1.118136088\r<BR>\n" );
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document.write( "p(z > -1.118136088) = .8682455167\r<BR>\n" );
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document.write( "round that to 3 decimal places and you get p(x > -1.118136088) = .868.\r<BR>\n" );
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document.write( "since the binomial distribution is discrete and the normal approximation is continuous, there is an adjustment that needs to be made.\r<BR>\n" );
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document.write( "that adjustment is to subtract .5 from the score and to add .5 to the score.\r<BR>\n" );
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document.write( "to find the probability of that score happening, you find the z-score for that score - .5 and the z-score for that score + .5 and then find the probability of getting between those z-score.\r<BR>\n" );
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document.write( "to find the probability of getting less than that score, you find the z-score for that score + .5 and then look for the probability that you can get below that z-score.\r<BR>\n" );
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document.write( "to find the probability of getting more than that score, you find the z-score for that score - .5 and then look for the probability that you can get above that z-score.\r<BR>\n" );
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document.write( "the last one is what we did.\r<BR>\n" );
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document.write( "the score was 265.<BR>\n" );
document.write( "we subtracted .5 from that to get 264.5.<BR>\n" );
document.write( "we calculated the z-score for (264.5 - 273.75) / 8.272696054.<BR>\n" );
document.write( "that gave us the z-score of -1.118136088.\r<BR>\n" );
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document.write( "we then looked for the probability that we would get a z-score greater than that.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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