Suppose that after extensive research you conclude

that the probability that the superhero will get bored after defeating any single criminal is 10%

independently of any others.

i. Find the expected value and standard deviation of the number of criminals that the superhero

will defeat in one night?

ii. The Superhero Union has a requirement for its members that they have to defeat at least

3500 villains in a year. Estimate the probability that our superhero will stay a member this

year.