Question

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?

Answer 1

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