document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1042677>Question 1042677</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1.	TekNaks is a new electronics outlet that promises expert sales-staff. TekNaks is examining their compensation package for the individual sales-person working in the 3-D TV department. Market research suggests that (during business hours) 3-D TV’s will sell at a rate of 0.25 units per hour (within the Ottawa outlet of interest). This question will focus on a typical 10am-8pm business day; entailing 10 business hours (the rate of TV unit sales can be considered constant throughout these business hours). <BR>\n" );
document.write( "a)	What is the expected number of sales per day? \r<BR>\n" );
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document.write( "b)	What is the variance of the number of sales per day? \r<BR>\n" );
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document.write( "c)	You have suggested a commission’s policy (as a way to provide an incentive to the sales-person). This would involve a commission of $50 per unit sold. You recognize that the sales-person’s income from commissions is a random variable. Calculate the following for that random variable (daily total commission). \r<BR>\n" );
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document.write( "i)	Expected value <BR>\n" );
document.write( "ii)	Coefficient of variation \r<BR>\n" );
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document.write( "d)	Management believes that a daily commission of $200 or more would be excessive compensation (note that a commission of $200 implies 4 sales). Calculate the probability of having four or more sales per day. \r<BR>\n" );
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document.write( "e)	Consider a particular work day in which the salesperson has made no sales from 10am until 3 pm (5 hours). Calculate the probability that the time until the next sale will be less than 5 hours.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #657697 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=657697\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Market research suggests that (during business hours) 3-D TV’s will sell at a rate of 0.25 units per hour (within the Ottawa outlet of interest). This question will focus on a typical 10am-8pm business day; entailing 10 business hours (the rate of TV unit sales can be considered constant throughout these business hours). <BR>\n" );
document.write( "a)	What is the expected number of sales per day?<BR>\n" );
document.write( "E(x) = 10*0.25 = 2.5 <BR>\n" );
document.write( "b)	What is the variance of the number of sales per day?<BR>\n" );
document.write( "S(x) = sqrt[n*p*q] = sqrt[10*0.25*0.75] = 1.37<BR>\n" );
document.write( "c)	You have suggested a commission’s policy (as a way to provide an incentive to the sales-person). This would involve a commission of $50 per unit sold. You recognize that the sales-person’s income from commissions is a random variable. Calculate the following for that random variable (daily total commission). <BR>\n" );
document.write( "i)	Expected value = 2.5*50 = $125 <BR>\n" );
document.write( "ii)	Coefficient of variation = (std)/(mean) = 1.37/125 = 0.011 <BR>\n" );
document.write( "d)	Management believes that a daily commission of $200 or more would be excessive compensation (note that a commission of $200 implies 4 sales). Calculate the probability of having four or more sales per day.<BR>\n" );
document.write( "z(4) = (4-2.5)/1.37 = 1.5/1.37 = 1.0949<BR>\n" );
document.write( "P(x >= 4) = P(z >= 1.0949) = normalcdf(1.0949,100) = 0.1368<BR>\n" );
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document.write( "e)	Consider a particular work day in which the salesperson has made no sales from 10am until 3 pm (5 hours). Calculate the probability that the time until the next sale will be less than 5 hours.<BR>\n" );
document.write( "Comment:: I'll leave that to you.<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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