SOLUTION: 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 depar

Question 1042677: 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).
a) What is the expected number of sales per day?
b) What is the variance of the number of sales per day?
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).
i) Expected value
ii) Coefficient of variation
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.

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.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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).
a) What is the expected number of sales per day?
E(x) = 10*0.25 = 2.5
b) What is the variance of the number of sales per day?
S(x) = sqrt[n*p*q] = sqrt[10*0.25*0.75] = 1.37
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).
i) Expected value = 2.5*50 = $125
ii) Coefficient of variation = (std)/(mean) = 1.37/125 = 0.011
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.
z(4) = (4-2.5)/1.37 = 1.5/1.37 = 1.0949
P(x >= 4) = P(z >= 1.0949) = normalcdf(1.0949,100) = 0.1368
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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.
Comment:: I'll leave that to you.
Cheers,
Stan H.
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