document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1134279>Question 1134279</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a survey of nursing students pursuing a master’s degree, 84 percent stated that they expect to be promoted to a higher position within one month after receiving the degree. If this percentage holds for the entire population, find, for a sample of 20, the probability that the number expecting a promotion within a month after receiving their degree is:<BR>\n" );
document.write( "a. Five                                               b. At least six<BR>\n" );
document.write( "c. No more than four                         d. Between five and eight, inclusive<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #751630 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=751630\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Use the Binomial Probability Formula<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Probability (P) (k successes in n trials) = nCk * p^(k) * (1-p)^(n-k), where nCk = n!/(k! * (n-k)!), p is probability of success<BR>\n" );
document.write( ":<BR>\n" );
document.write( "For this problem, p = 0.84, n = 20<BR>\n" );
document.write( ":<BR>\n" );
document.write( "a) P (k = 5, n = 20) = 20C5 * (0.84)^5 * (1-0.84)^(20-5) = 0.000001<BR>\n" );
document.write( ":<BR>\n" );
document.write( "b) P (k > or = 6, n = 20) = 1 - (summation i = 0 to 5 of P(k = i, n = 20) = 0.999999<BR>\n" );
document.write( ":<BR>\n" );
document.write( "c) P (k < or = 4, n = 20) = summation i = 0 to 4 of P(k = i, n = 20) = 0.000001<BR>\n" );
document.write( ":<BR>\n" );
document.write( "d) P (5 < or = k < or = 8, n = 20) = summation i = 5 to 8 of P(k = i, n = 20) =  0.000012<BR>\n" );
document.write( ":<BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );