According to the Guinness Book of World Records (2005), the fastest pumpkin-carver on record, Steven Clarke, carved 42 pumpkins an hour. Assume this is his average rate. Let X be the number of pumpkins Steven carves in an hour. (We suppose that the carver can steadily maintain work at his record rate.)
a. Assume that this a Poisson situation. What is the parameter?
b. What is the probability Steven will carve exactly 40 pumpkins in the hour?
c. Given that he has carved at least 3 pumpkins in a 5-minute interval, what he probability that he will carve at least 4 pumpkins during that 5-minute interval?
d. Given that he carves fewer than 4 pumpkins in a 5-minute interval, at is the probability he carves fewer than 2 pumpkins during that 5-minute interval?
e. What is the expected number of pumpkins he can carve in 3 minutes at pace?
f. Show the labeled graph of the mass for pumpkins carved in a 3-minute al.
g. Show the labeled graph of the CDF for pumpkins carved in a 3-minute interval.