Practice FT3 Q8 - Looking for a detailed, worked solution with theoretical explanation

Artificial Intelligence enthusiast Sam has been training his bot to play the relatively unknown online game Among Us. But his bot has always been "too sus" (too suspicious). As an experiment Sam decides to make the bot roll a (virtual) 7-sided die before doing anything suspicious. The bot does something suspicious on a roll of one, and othewise pretends to be normal In their super long custom gamemode, Sam's bot has 200 opportunities to do something suspicious (sabotage, kill crewmates, lie at meetings). a) Let X be the number of times that Sam's bot is suspicious. Calculate the following E(X) = Var(X) = b) Sam discovers his bot will only win if it can keep the number of "sus"-activities less than or equal to 25 events per game. If Sam's bot plays 1000 games, then how many games would Sam expect his bot to win? Without using a continunity correction, find the expected number of non-sus games (i.e. games won) out of 1000: Briefly explain the process you used to find the expect number of games won. Insert explanation Standard normal probabilities P(Z