Statistics Question

Question

Type | Probability

1 ton | 0.25

2 tons | 0.06

5 tons | 0.01

10 tons | 0.11

20 tons | 0.57

 

 

An appliance dealer sells 5 types of air conditioners. The above gives the distribution of the random variable X - tonnage of air conditioner bought by a customer

 

The air conditioners are priced by the retailer at 200 dollars per ton. The retailer pays 100 dollars per ton to buy the air conditioners. In addition there is an overhead cost of 50 dollars per air conditioner. What is the expected value of the profit for the retailer from the sale of an air conditioner?

Answer 1

[$200(1 ton)-$100(1 ton)-$50](.25)=12.5

[$200(2 ton)-$100(2 ton)-$50](.06)=9

[$200(5 ton)-$100(5 ton)-$50](.01)=4.5

[$200(10 ton)-$100(10 ton) -$50](.11)=104.5

[$200(20 ton) - $100(20 ton) -$50](.57)=1111.5

 

12.5+9+4.5+104.5+1111.5= $1242 expected profit