Joey hears of a different type of Rattata in Alola. So, he takes a long-term trip to catch this new type of the Pokmon Rattata. While in Alola, he encounters a mean of 14 Alolan Rattata each day. Round answers to four decimal places.

What is the probability that Joey encounters 7 Alolan Rattata on a particular day of his trip? (Round to four decimal places)

Joey finds out more Alolan Rattata are encountered at night. What is the probability that Joey encounters at least 20 Alolan Rattata one night, assuming the mean stays the same?

On the last day of his trip, Joey finds out that he is limited on how many more Pokmon he can take with him on the plane. What is the probability that on his last day he catches less than 15 Alolan Rattata?