Question

Sam is a representative who sells large appliances such as refrigerators, stoves, and so forth. Let x = number of appliances Sam sells on a given day and let P(X) represent the probability of that many sales on a given day.

X	P(X)
0	0.20
1	0.25
2	0.20
3	0.35

Assume that the sales record is representative of the population of all sales days.(a) Compute the probability that x is between 1 and 3 (including 1 and 3).

(b) Compute the probability that x is strictly less than 3.

(c) Compute the expected value of the x distribution.

____________________________

____________________________

____________________________

(d) Compute the standard deviation of the x distribution. HINT: ? = √∑ ?2 ∙ ?(?) − ?2____________________________

(e) Create a histogram for the probability distribution in #15 on the previous page.

Answer 1

a)

P(1<=x<=3) =0.25+0.2+0.35 =0.8

b)

P(X<3) =P(x=0)+P(X=1)+P(x=2) =0.2+0.25+0.2 =0.65

c)

E(x) =μ=

ΣxP(x) =0*0.2+1*0.25+2*0.2+3*0.35 =1.70

d)

E(x2) =	Σx2P(x) =0^2*0.2+1^2*0.25+2^2*0.2+3^2*0.35	4.2000
Var(x)=σ2 =	E(x2)-(E(x))2=4.2-1.7^2 =	1.31
std deviation=	σ= √σ2 =sqrt(1.31) =	1.14455

e)