document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=74029>Question 74029</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Geometric and Binomial trials<BR>\n" );
document.write( "Geometric: E(X)=1/p       SD(X)=square root of q/p^2<BR>\n" );
document.write( "Binomial:  E(X)=np         SD(X)=square root of npq\r<BR>\n" );
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document.write( "1.  in a bowling league, the mean score for men is 154 qith a standard deviation(SD) of 9...for women it is a mean of 144 with a standard deviation of 12.  at the end, they randomly pair men and women as opponets<BR>\n" );
document.write( "a)what is the expected total of men and women pairs?\r<BR>\n" );
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document.write( "b)what is the Standard Deviation of the sum of the pairs?\r<BR>\n" );
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document.write( "2.  18% of adults are smokers<BR>\n" );
document.write( "a)they selected a few adults at random to find out if they are smokers.  explain why this is a Bernoulli trial?\r<BR>\n" );
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document.write( "b)how many people do you expect to ask to find a smoker?\r<BR>\n" );
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document.write( "c)whats the probability that there are at least 8 smokers among a sample of 30 people?\r<BR>\n" );
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document.write( "3.  70% of drivers wear seatbelts.  there was a random sample of 500 drivers taken.<BR>\n" );
document.write( "a)use a Binomial model to find the probablity that at least 350 drivers are wearing seatbelts?\r<BR>\n" );
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document.write( "b)use a Binomial model to find the probablity that no more than 400 drivers are wearing seatbelts?\r<BR>\n" );
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document.write( "im very lost on these problems so if you could help, id be so greatful! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #53123 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=53123\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Geometric and Binomial trials<BR>\n" );
document.write( "Geometric: E(X)=1/p; SD(X)=square root of q/p^2<BR>\n" );
document.write( "Binomial: E(X)=np; SD(X)=square root of npq \r<BR>\n" );
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document.write( "1. in a bowling league, the mean score for men is 154 with a standard deviation(SD) of 9...for women it is a mean of 144 with a standard deviation of 12. at the end, they randomly pair men and women as opponets<BR>\n" );
document.write( "a)what is the expected total score of men and women pairs?<BR>\n" );
document.write( "For the men:<BR>\n" );
document.write( "mean=np = 154; std=sqrt(npq)=9<BR>\n" );
document.write( "So, std=sqrt(154q)=9<BR>\n" );
document.write( "Square both sides to get 154q=81<BR>\n" );
document.write( "q=81/154; therefore p=73/154<BR>\n" );
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document.write( "For the women:<BR>\n" );
document.write( "mean=np=144; std=sqrt12<BR>\n" );
document.write( "So, std=sqrt(144q)=12<BR>\n" );
document.write( "Square both sides to get 144q=144<BR>\n" );
document.write( "q=1 and p=0<BR>\n" );
document.write( "COMMENT: This does not make sense.<BR>\n" );
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document.write( "b)what is the Standard Deviation of the sum of the pairs? <BR>\n" );
document.write( "If std=9, Var=81<BR>\n" );
document.write( "If std=12, Var=144<BR>\n" );
document.write( "std(men+women)=sqrt(81+144)= 15<BR>\n" );
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document.write( "2. 18% of adults are smokers<BR>\n" );
document.write( "a)they selected a few adults at random to find out if they are smokers. explain why this is a Bernoulli trial? <BR>\n" );
document.write( "Two possible outcomes: smoker or no smoker<BR>\n" );
document.write( "Smoking among the people selected may not be independent but they<BR>\n" );
document.write( "are less then 10% of the total population.<BR>\n" );
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document.write( "b)how many people do you expect to ask to find a smoker?<BR>\n" );
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document.write( "c)whats the probability that there are at least 8 smokers among a sample of 30 people? <BR>\n" );
document.write( "n=30,p=0.18,X>=8<BR>\n" );
document.write( "If you have a TI calculator use [1- binomcdf(30,0.18,7)]=0.158...<BR>\n" );
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document.write( "3. 70% of drivers wear seatbelts. there was a random sample of 500 drivers taken.<BR>\n" );
document.write( "a)use a Binomial model to find the probablity that at least 350 drivers are wearing seatbelts?<BR>\n" );
document.write( "n=500; p=0.7; X>=350<BR>\n" );
document.write( "Use [1-binomcdf(500,0.7,349)]=0.522<BR>\n" );
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document.write( "b)use a Binomial model to find the probablity that no more than 400 drivers are wearing seatbelts? <BR>\n" );
document.write( "X<=400<BR>\n" );
document.write( "Use binomcdf(500,0.7,400)=0.999999<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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