An online shopping website develops new features and iterates on its

product recommendations on a regular basis. The team also uses an experiment when launching each new

feature to assess the impact of the change on the total sales. Below is a summary table of the impacts that

the team observes:

Number of Sales From Launch $-2000+200+500$

Proportion of Launches $0\mathrm{.}10\mathrm{.}50\mathrm{.}30\mathrm{.}1$

$($a$)$ Compute the average impact for the experiments.

$($b$)$ Compute the standard deviation of the impact from these experiments.