document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1031950>Question 1031950</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The time that customers take to complete their transaction at a money machine is a random variable with mean of 2 minutes and a standard deviation of 0.6 minutes. Assume the variable is normally distributed.\r<BR>\n" );
document.write( "\n" );
document.write( "a)	What is the probability that a randomly selected customer will take between 1.5 and 2.5 minutes to complete his transaction?<BR>\n" );
document.write( "b)	Find the probability that a random sample of 50 customers will take more than 112 minutes to complete all their transactions <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 #646663 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=646663\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  The time that customers take to complete their transaction at a money machine is a random variable with mean of 2 minutes and a standard deviation of 0.6 minutes. Assume the variable is normally distributed. <BR>\n" );
document.write( "a)	What is the probability that a randomly selected customer will take between 1.5 and 2.5 minutes to complete his transaction?<BR>\n" );
document.write( "---<BR>\n" );
document.write( "z(1.5) = (1.5-2)/0.6 = -0.8333<BR>\n" );
document.write( "z(2.5) = (2.5-1.5)/0.6 = 1/0.6 = 10/6 = 5/3<BR>\n" );
document.write( "---<BR>\n" );
document.write( "P(1.5< x < 2.5) = P(-0.8333< z < 5/3) = normalcdf(-0.8333,5/3) = 0.7500<BR>\n" );
document.write( "=============================<BR>\n" );
document.write( "b)	Find the probability that a random sample of 50 customers will take more than 112 minutes to complete all their transactions<BR>\n" );
document.write( "z(112) = (112-2)/(0.6/sqrt(50)) = 1296<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Note:: I suspect there is a typo in your post.<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "----------------  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );