Question 1042677
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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