Protocol droids arrive in General Organa's quarters at an average rate of 5 droids every 2 minutes. If the arrival of droids assumes a Poisson distribution, calculate the following:
- What is the probability that exactly 4 droids will arrive in 2 minutes?
- What is the probability that fewer than 5 will arrive in 4 minutes?
- What is the probability that 9 or more will arrive in 2 minutes?
- What is the probability that no droids will arrive in 1 minute?
- If the probability that a droid arrives is 0.04% and we have a sample of 250 droids, what is the standard deviation of the Poisson distribution.