Answer to Question #209895 in Statistics and Probability for Rajib

Question

Alex Mason has a wide-curving, uphill driveway leading to his garage. When there is a heavy snow, Alex hires a local carpenter, who shovels snow on the side in the winter, to shovel his driveway. The snow shoveler charges $30 to shovel the driveway. Following is a probability distribution of the number of heavy snows each winter.

Heavy Snows

Probability

1

1.12

2

0.19

3

0.24

4

0.22

5

0.13

Alex is considering the purchase of a new self-propelled snow blower for $575 that would allow him, his wife, or his children to clear the driveway after a snow. Discuss what you think Alex's decision should be and why.

Answer 1

$$\def\arraystretch{1.5} \begin{array}{c:c} Heavy\ Snows & Probability \\ \hline 1 & 0.12\\ 2 & 0.19\\ 3 & 0.24\\ 4 & 0.22\\ 5 & 0.13\\ 6 & 0.08\\ 7 & 0.02\\ \hdashline & 1.00\\ \end{array}$$

What is the annual expected cost of shoveling snow?

$$30(1(0.12)+2(0.19)+3(0.24)+4(0.22)$$

$$+5(0.13)+6(0.08)+7(0.02))=101.10$$

How many winters would it take to completely payback the purchase of a snow blower?

$$\dfrac{575}{101.10}=6$$

6 years would it take to completely payback the purchase of a snow blower.