document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1091257>Question 1091257</A>: <I><SPAN STYLE=\"word-break: break-all;\"> you are told that there is an 80% chance that a prospective employer will check the educational background of a job applicant. 75 job applications are randomly selected.\r<BR>\n" );
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document.write( "A. find the probability that at least 50 of the applicants have their educational backgrounds checked\r<BR>\n" );
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document.write( "B. find the probability that exactly 50 of the applicants have their educational backgrounds checked </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #705651 by </B><A HREF=/tutors/aboutme.mpl?userid=mathmate><B>mathmate(429)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mathmate><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=mathmate><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=705651\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Question:<BR>\n" );
document.write( "you are told that there is an 80% chance that a prospective employer will check the educational background of a job applicant. 75 job applications are randomly selected.<BR>\n" );
document.write( "A. find the probability that at least 50 of the applicants have their educational backgrounds checked<BR>\n" );
document.write( "B. find the probability that exactly 50 of the applicants have their educational backgrounds checked<BR>\n" );
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document.write( "Solution:\r<BR>\n" );
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document.write( "Since the probability of success (checking educational background) is constant throughout, sampling is random, and size of sample is known, we can model using the binomial distribution.<BR>\n" );
document.write( "P(x)=C(n,x)p^x*(1-p)^(n-x)<BR>\n" );
document.write( "with C(n,x)=n!/(x!(n-x)!)  number of combinations of x objects taken out of n.<BR>\n" );
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document.write( "Here, n=75, x=50, p=0.8<BR>\n" );
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document.write( "(B) exactly 50 applicants (out of 75) have their backgrounds checked:<BR>\n" );
document.write( "P(X=50)=C(75,50)*(0.8^50)(0.2^25)<BR>\n" );
document.write( "=52588547141148893628*1.427247692705967*10^-5*3.355443200000008*10^-18<BR>\n" );
document.write( "= 0.00251849<BR>\n" );
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document.write( "(A) At least 50 applicants<BR>\n" );
document.write( "P(X>=50)=P(X=50)+P(x=51)+P(X=52)+...+P(x=75)<BR>\n" );
document.write( "=0.0025185+0.0049382+0.0091167+0.0158252+0.0257893<BR>\n" );
document.write( "+0.0393872+0.0562675+0.0750233+0.0931324+0.1073390<BR>\n" );
document.write( "+0.1144950+0.1126180+0.1017195+0.0839589+0.0629692<BR>\n" );
document.write( "+0.0426253+0.0258335+0.0138807+0.0065321+0.0026507<BR>\n" );
document.write( "+0.0009088+0.0002560+0.0000569+0.0000094+0.0000010<BR>\n" );
document.write( "+0.0000001<BR>\n" );
document.write( "=0.9978525<BR>\n" );
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document.write( "Since the above calculation is quite tedius, in most cases, solution is obtained using the normal approximation.<BR>\n" );
document.write( "mean=75*0.8=60<BR>\n" );
document.write( "variance=75*0.8*0.2=12<BR>\n" );
document.write( "standard deviation = sqrt(12)<BR>\n" );
document.write( "Applying the continuity correction,<BR>\n" );
document.write( "Z=(49.5-60)/sqrt(12)=-3.0311<BR>\n" );
document.write( "P(Z>49.5)<BR>\n" );
document.write( "=1-P(Z>49.5)<BR>\n" );
document.write( "=1-0.001218367<BR>\n" );
document.write( "=0.9987816<BR>\n" );
document.write( "with an error of -0.093%<BR>\n" );
document.write( " </SPAN>\n" );
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