Compute the probability of only one candidate arriving in 2-hour interval of time.

Question description

candidates arrive at ABC company for job interview at the rate of 3 per hour.

The number of candidates arriving follows a Poisson distribution:

Where,

𝑓(𝑥) = the probability of 𝑥 candidates arriving in an interval

𝜇 = mean number of candidates arriving in an interval

a. Compute the probability of exactly 5 candidates arriving in 6-hour interval of time

b. Compute the probability of at most 2 candidates arriving in 6-hour interval of time

c. Compute the probability of only one candidate arriving in 2-hour interval of time.