Make sure to clearly define the random variables and specify their probability distributions and parameters.

Use R for computations in the following questions and submit your R file as well.

A coffee shop serves an average of 75 customers per hour during the morning rush.

(a) Which distribution we have studied is most appropriate for calculating the probability

of a given number of customers arriving within one hour during this time of day?

(b) What are the mean and the standard deviation of the number of customers this coffee

shop serves in one hour during this time of day?

(c) Would it be considered unusually low if only 60 customers showed up to this coffee

shop in one hour during this time of day?

(d) Calculate the probability that this coffee shop serves 70 customers in one hour during

this time of day?