Question

In: Math

13) A logging truck sales representative can contact either one or two potential buyers per day...

13) A logging truck sales representative can contact either one or two potential buyers per day with probabilities of 0.25 and 0.75, respectively. Each contact will result in either no sale or a $75,000 sale with probabilities of 0.85 and 0.15, respectively(hint: start with a tree diagram)

a) Show the probability distribution of daily sales.

b) What is the expected value of daily sales?

c) What is the standard deviation of daily sales?

Solutions

Expert Solution

a)let x is randomly distributed sale on a given day.

below is probability distribution of daily sales

P(X=0)=P(contact one buyer and no sale)+P(contact two buyer and no sale on both)=0.25*0.85+0.75*0.85*0.85=0.7544

P(X=75000)=P(contact one buyer and one sale)+P(contact two buyer and one sale)=0.25*0.15+0.75*2C10.85*0.15=0.2288

P(X=150000)=P(contact two buyer and two sale)=0.75*0.15*0.15=0.0169

b)

x f(x) xP(x) x2P(x)
0.0000 0.7544 0.000 0.000
75000.0000 0.2288 17156.250 1286718750.000
150000.0000 0.0169 2531.250 379687500.000
total 19687.500 1666406250.000
E(x) =μ= ΣxP(x) = 19687.5000
E(x2) = Σx2P(x) = 1666406250.0000
Var(x)=σ2 = E(x2)-(E(x))2= 1278808593.7500
std deviation=         σ= √σ2 = 35760.4334

expected value of daily sales =19687.50

c)

standard deviation of daily sales =36760.43


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