Question

If The probabilities that a customer selects 1, 2, 3, 4, and 5 items at a convenience store are 0.32, 0.12, 0.23, 0.18, and 0.15, respectively,

a) construct a probability distribution for the data and draw a graph for the distribution

b) Find the mean and standard deviation for the probability distribution

c) What is the probability that a customer will select 3 or more items at a convenience store?

Answer 1

a)below is probability distribution for the number of items selected by customer

x	P(X=x)
1	0.320
2	0.120
3	0.230
4	0.180
5	0.150

b)

mean E(X) =ΣxP(x) =1*0.32+2*0.12+3*0.23+4*0.18+5*0.15 =2.72

E(X²)=Σx²P(x) =1^2*0.32+2^2*0.12+3^2*0.23+4^2*0.18+5^2*0.15 =9.50

standard deviation =sqrt(E(X²)-(E(X))²) =sqrt(9.5-2.72^2)=1.450

c)probability that a customer will select 3 or more items at a convenience store

=P(X>=3) =P(X=3)+P(X=4)+P(X=5)=0.23+0.18+0.15 = 0.56