An ornothologist $($a bird scientist$)$ is spending one hour each day bird watching around the habitat of a rare finch. They spot on average about $87$ birds each day but only $6$ of them are finches. Keep in mind that the rate is expressed per hour but some of the following questions relate to the number of minutes.

a$)$ What is the probability that the researcher spots between $80$ and $100$ birds $($inclusive$)$ during an hour of observation. 

b$)$ What is the probability that the researcher spots between $8$ and $10$ finches $($inclusive$)$ during an hour of observation.

c$)$ If the researcher spots a total of $95$ birds during a shift, what is the probability that at least $7$ of them are finches? 

d$)$ What is the probability that the researcher spots less than $4$ finches on a given day? 

e$)$ What is the probability that the researcher does not spot $4$ or more finches $($per day$)$ at least once in the next $3$ days?

f$)$ How many minutes does the researcher expect to wait before spotting their first finch? 

g$)$ What is the probability that the researcher waits $20$ or more minutes to spot their first finch on a given shift? 

h$)$ What is the probability that the researcher waits $60$ or more minutes to spot their first finch on a given shift? 

i$)$ What is the probability that they spots $0$ finches on a given shift?