document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=730800>Question 730800</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose 80% of all college students who own cell phones send and receive text messages.  In a random sample of 10 cell-phone owners, what is the probability that A) 8 of these student send and receive text messages and B) at least 7 of these students send and receive text messages?\r<BR>\n" );
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document.write( "I know that p=.8, and that the n for A is 8.  But I can't figure out the rest.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #446848 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=446848\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Both parts will use the binomial distribution probability formula, which is\r<BR>\n" );
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document.write( "P(X = k) = (n C k)*(p)^(k)*(1-p)^(n-k)\r<BR>\n" );
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document.write( "for both parts A and B, n = 10 and p = 0.8\r<BR>\n" );
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document.write( "A)\r<BR>\n" );
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document.write( "For this part A) only, k = 8\r<BR>\n" );
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document.write( "P(X = k) = (n C k)*(p)^(k)*(1-p)^(n-k)\r<BR>\n" );
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document.write( "P(X = 8) = (10 C 8)*(0.8)^(8)*(1-0.8)^(10-8)\r<BR>\n" );
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document.write( "P(X = 8) = (10 C 8)*(0.8)^(8)*(0.2)^(10-8)\r<BR>\n" );
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document.write( "P(X = 8) = (45)*(0.8)^(8)*(0.2)^2\r<BR>\n" );
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document.write( "P(X = 8) = (45)*(0.167772)*(0.04)\r<BR>\n" );
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document.write( "P(X = 8) = <font color=\"red\">0.30199</font>\r<BR>\n" );
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document.write( "So the probability that exactly 8 students sent and received text messages is roughly <font color=\"red\">0.30199</font>\r<BR>\n" );
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document.write( "B)\r<BR>\n" );
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document.write( "For this part, we need to find P(X = 7), P(X = 8), P(X = 9), and P(X = 10). We will add them up to calculate P(X >= 7)\r<BR>\n" );
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document.write( "P(X = k) = (n C k)*(p)^(k)*(1-p)^(n-k)\r<BR>\n" );
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document.write( "P(X = 7) = (10 C 7)*(0.8)^(7)*(1-0.8)^(10-7)\r<BR>\n" );
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document.write( "P(X = 7) = (10 C 7)*(0.8)^(7)*(0.2)^(10-7)\r<BR>\n" );
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document.write( "P(X = 7) = (120)*(0.8)^(7)*(0.2)^3\r<BR>\n" );
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document.write( "P(X = 7) = (120)*(0.209715)*(0.008)\r<BR>\n" );
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document.write( "P(X = 7) = 0.201327\r<BR>\n" );
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document.write( "P(X = k) = (n C k)*(p)^(k)*(1-p)^(n-k)\r<BR>\n" );
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document.write( "P(X = 8) = (10 C 8)*(0.8)^(8)*(1-0.8)^(10-8)\r<BR>\n" );
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document.write( "P(X = 8) = (10 C 8)*(0.8)^(8)*(0.2)^(10-8)\r<BR>\n" );
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document.write( "P(X = 8) = (45)*(0.8)^(8)*(0.2)^2\r<BR>\n" );
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document.write( "P(X = 8) = (45)*(0.167772)*(0.04)\r<BR>\n" );
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document.write( "P(X = 8) = 0.30199\r<BR>\n" );
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document.write( "P(X = k) = (n C k)*(p)^(k)*(1-p)^(n-k)\r<BR>\n" );
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document.write( "P(X = 9) = (10 C 9)*(0.8)^(9)*(1-0.8)^(10-9)\r<BR>\n" );
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document.write( "P(X = 9) = (10 C 9)*(0.8)^(9)*(0.2)^(10-9)\r<BR>\n" );
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document.write( "P(X = 9) = (10)*(0.8)^(9)*(0.2)^1\r<BR>\n" );
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document.write( "P(X = 9) = (10)*(0.134218)*(0.2)\r<BR>\n" );
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document.write( "P(X = 9) = 0.268435\r<BR>\n" );
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document.write( "P(X = k) = (n C k)*(p)^(k)*(1-p)^(n-k)\r<BR>\n" );
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document.write( "P(X = 10) = (10 C 10)*(0.8)^(10)*(1-0.8)^(10-10)\r<BR>\n" );
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document.write( "P(X = 10) = (10 C 10)*(0.8)^(10)*(0.2)^(10-10)\r<BR>\n" );
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document.write( "P(X = 10) = (1)*(0.8)^(10)*(0.2)^0\r<BR>\n" );
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document.write( "P(X = 10) = (1)*(0.107374)*(1)\r<BR>\n" );
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document.write( "P(X = 10) = 0.107374\r<BR>\n" );
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document.write( "So in short, we found this\r<BR>\n" );
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document.write( "P(X = 7)= 0.201327<BR>\n" );
document.write( "P(X = 8)= 0.30199<BR>\n" );
document.write( "P(X = 9)= 0.268435<BR>\n" );
document.write( "P(X = 10)= 0.107374\r<BR>\n" );
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document.write( "They add to...\r<BR>\n" );
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document.write( "P(X >= 7) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)\r<BR>\n" );
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document.write( "P(X >= 7) = 0.201327 + 0.30199 + 0.268435 + 0.107374 \r<BR>\n" );
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document.write( "P(X >= 7) = <font color=\"red\">0.879126</font>\r<BR>\n" );
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document.write( "So the probability that at least 7 of these students send and receive text messages is approximately <font color=\"red\">0.879126</font><BR>\n" );
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