document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=205386>Question 205386</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. At a house, there are 6 seniors, 4 juniors, and 2 sophomores. If a committee of 3 is selected at random, what is the probability that 1 sophomore and 2 seniors will be selected?\r<BR>\n" );
document.write( "\n" );
document.write( "2. The average repair cost of a microwave oven is $55, with a standard deviation of $8. The costs are normally distributed. If 12 ovens are repaird, find the probability that the mean of the repair bills will be less than $51.\r<BR>\n" );
document.write( "\n" );
document.write( "3. A researcher at Wilkes University wishes to estimate the average amount of money earned by all students who work summer jobs. The standard deviation is known to be $500. In a random sample of 60 Wilkes students who had summre jobs, the researcher found the mean amount of money they earned to be $3000. Find the 95% confidence interval for the mean amount of money earned by all students with summer jobs. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #155058 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=155058\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. At a house, there are 6 seniors, 4 juniors, and 2 sophomores. If a committee of 3 is selected at random, what is the probability that 1 sophomore and 2 seniors will be selected?<BR>\n" );
document.write( "---<BR>\n" );
document.write( "# of ways to get the committee as described: 2 = 2*15 = 30<BR>\n" );
document.write( "---<BR>\n" );
document.write( "# of ways to pick the committee without condition: 12C3 = (12*11*10/(1*2*3)<BR>\n" );
document.write( "= 220<BR>\n" );
document.write( "---------------------------<BR>\n" );
document.write( "Probability of picking the committee as described = 30/220 = 3/22<BR>\n" );
document.write( "=========================================================================<BR>\n" );
document.write( " <BR>\n" );
document.write( "2. The average repair cost of a microwave oven is $55, with a standard deviation of $8. The costs are normally distributed. If 12 ovens are repaird, find the probability that the mean of the repair bills will be less than $51.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "z(51) = (51-55)/[8/sqrt(12)] = -1.732...<BR>\n" );
document.write( "---<BR>\n" );
document.write( "P(x < 51) = P(z<-1.732) = 0.0416<BR>\n" );
document.write( "=========================================================================<BR>\n" );
document.write( " <BR>\n" );
document.write( "3. A researcher at Wilkes University wishes to estimate the average amount of money earned by all students who work summer jobs. The standard deviation is known to be $500. In a random sample of 60 Wilkes students who had summer jobs, the researcher found the mean amount of money they earned to be $3000. Find the 95% confidence interval for the mean amount of money earned by all students with summer jobs.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "sample mean = 3000<BR>\n" );
document.write( "E = 1.96*500/sqrt(60)= 126.52<BR>\n" );
document.write( "------<BR>\n" );
document.write( "95% CI : 3000-126.52 < u < 3000+126.52<BR>\n" );
document.write( "==========================================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );