document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197417>Question 1197417</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sun Courier  -  a parcel delivery company  -  has found that the delivery time of parcels <BR>\n" );
document.write( "to clients in Durban metropolitan area after airport collection is normally distributed <BR>\n" );
document.write( "with a mean delivery time equal to 45 minutes and a standard deviation of 8 minutes. <BR>\n" );
document.write( "For a newly arrived consignment at Durban airport, what is the probability that a <BR>\n" );
document.write( "randomly selected parcel will take:<BR>\n" );
document.write( "a. Between 45 and 51 minutes to deliver to the client?<BR>\n" );
document.write( "b. Less than 48 minutes to deliver? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #830674 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=830674\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> z = (x - m) / s<BR>\n" );
document.write( "z is the z-score<BR>\n" );
document.write( "x is the raw score<BR>\n" );
document.write( "m is the mean<BR>\n" );
document.write( "s is the standard deviation.<BR>\n" );
document.write( "you have:<BR>\n" );
document.write( "m = 45<BR>\n" );
document.write( "s = 8<BR>\n" );
document.write( "when x = 45, z = (45 - 45) / s = 0<BR>\n" );
document.write( "when x = 51, z = (51 - 45) / s = 6 / 8 = 3/4 = .75<BR>\n" );
document.write( "area to the left of z = 0 = .5<BR>\n" );
document.write( "area to the left of z = .75 = .7734 rounded to 4 decimal places.<BR>\n" );
document.write( "area in between z = 0 and z = .75 = .7734 - .5 = .2734.<BR>\n" );
document.write( "that's the probability that the package will take between 45 and 51 minutes to deliver to the client. \r<BR>\n" );
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document.write( "when x = 48, z = (x - m) / s becomes z = (48 - 45) / 8 which becomes z = 3 / 8 = .375.<BR>\n" );
document.write( "area to the left of z = .375 = .6462 rounded to 4 decimal places.<BR>\n" );
document.write( "that's the probability that the package will take less than 48 minutes to deliver to the client.\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );