Supercell is a maker of mobile games. They have found that the amount of money a new player spends on one of their games during their first year of play is between a minimum of $0 and a maximum of $52, with all values equally likely (not restricted to whole numbers). (They have rules that prevent players from spending more than $52 dollars).

a. What is the distribution of the amount of money a player will spend during their first year of play?

b. What is the expected amount of money and standard deviation of the amount of money a player will spend during their first year of playing?

c. In exchange for their real-world dollars (USD), players purchase an in-game currency to spend on various options and advantages inside the game. Assuming a player can purchase any amount (so not restricted to whole numbers) of this in-game currency, limited only by the $52 cap on purchases, at an exchange rate of 27.4 of the in-game currency for every real-world dollar. What is the standard deviation of the amount of in-game currency a player will purchase during their first year of play.

d. What is the probability a new player purchases between 602.8 and 1,233 (inclusive) of in-game currency?