document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=142057>Question 142057</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help understanding this problem. I am lost<BR>\n" );
document.write( "In the Ardmore Hotel, 20 percent of the customers pay by American Express credit card. (a) Of the next 10 customers, what is the probability that none pay by American Express? (b) At least two? (c) Fewer than three? (d) What is the expected number who pay by American Express? (e) Find the Standard deviation. <BR>\n" );
document.write( "Any help would be great. Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #103463 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=103463\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In the Ardmore Hotel, 20 percent of the customers pay by American Express credit card.<BR>\n" );
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document.write( "Comment: This is a binomial problem with mean = np = 20*0.2 = 4 and <BR>\n" );
document.write( "standard deviation sqrt(npq) = sqrt(20*0.2*0.8) = sqrt(3.2) = 1.7889<BR>\n" );
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document.write( "P(pay by AE) = 0.2 ; P(do not pay by AE)= 0.8<BR>\n" );
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document.write( "(a) Of the next 10 customers, what is the probability that none pay by American Express?<BR>\n" );
document.write( "p(none in 10) = 0.8^10 = 0.10737...<BR>\n" );
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document.write( "(b) At least two? <BR>\n" );
document.write( "Comment: \"at least\" is a key word in binomial problems.  On this problem<BR>\n" );
document.write( "you have to understand the following:<BR>\n" );
document.write( "P(none pay) + P(one pays) + P(at least two pay) = 1<BR>\n" );
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document.write( "P(at least two) = 1 - [P(none) + P(one pay)<BR>\n" );
document.write( "= 1 - [0.10737 + 20C1(0.2)^1*(0.8)^19] = 1 - [0.10737+0.05765] = 0.8350<BR>\n" );
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document.write( "(c) Fewer than three?<BR>\n" );
document.write( "= P(one) + P(two) = 1- 0.8350 = 0.1650<BR>\n" );
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document.write( "(d) What is the expected number who pay by American Express?<BR>\n" );
document.write( "mean = np = 20*0.2 = 4<BR>\n" );
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document.write( "(e) Find the Standard deviation. <BR>\n" );
document.write( "sqrt(npq) = sqrt(4* 0.8) = sqrt(3.2) = sqrt(1.6*2) = 0.8sqrt(2)<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
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