Question Type 2: Finding the probability of some event given some contextual information of a poisson distribution Exercises

Assume that help calls arrive at a police station according to a Poisson process with an average of one call every 7 minutes. What is the probability that exactly one call is received in 7 minutes?

Assume that help calls arrive at a police station according to a Poisson process with an average of one call every 7 minutes. What is the probability that no calls are received in 3 minutes?

Assume that help calls arrive at a police station according to a Poisson process with an average of one call every 7 minutes. What is the probability that at most 1 call is received in 7 minutes?

Assume that help calls arrive at a police station according to a Poisson process with an average of one call every 7 minutes. What is the probability that exactly 3 calls are received in 10 minutes?

Assume that help calls arrive at a police station according to a Poisson process with an average of one call every 7 minutes. What is the probability that no calls are received in 14 minutes?

Assume that help calls arrive at a police station according to a Poisson process with an average of one call every 7 minutes. Find the probability that at least 2 calls are received in 10 minutes.

Assume that help calls arrive at a police station according to a Poisson process with an average of one call every 7 minutes. What is the probability that exactly 4 calls are received in 28 minutes?

Assume that help calls arrive at a police station according to a Poisson process with an average of one call every 7 minutes. Find the mean and variance of the number of calls received in 20 minutes.

Assume that help calls arrive at a police station according to a Poisson process with an average of one call every 7 minutes. What is the probability that more than 4 calls are received in 35 minutes?

Assume that help calls arrive at a police station according to a Poisson process with an average of one call every 7 minutes. What is the probability that between 2 and 4 calls inclusive are received in 35 minutes?

Assume that help calls arrive at a police station according to a Poisson process with an average of one call every 7 minutes. Given that the probability of receiving zero calls in $t$ minutes is 0.5, find $t$.

Assume that help calls arrive at a police station according to a Poisson process with an average of one call every 7 minutes. Find the minimum time $t$ such that the probability of receiving at least one call in $t$ minutes is at least 0.95.

Assume that help calls arrive at a police station according to a Poisson process with an average of one call every 7 minutes. What is the probability of receiving between 15 and 20 calls inclusive in a 2-hour period?