Suppose the number of customers arrive at a store follows a Poisson distribution with λ = 10 customers per hour.
a. What is the average time (in hour) until the first customer arrives?
b. What is the distribution of time (in hour) until the second customer arrives? Provide your answer with its correct parameter value.
c. Find the probability that one must wait for at least 0.5 hour until the second customer arrives.
d. Using a suitable approximation, find the probability of having more than 25 customers arriving at a store in 2 hours.