A call center company is interested in modeling the number of calls that they receive in a 10 minute interval in order to determine how many operators to hire. The "callcenterdata.txt" below contains the some data they collected in the month of October on the number of calls received in 10 minute intervals.

4,9,8,10,11,11,14,10,5,15,10,7,7, 10,9,6,6,4,5,10,7,3,2,1,6,8, 13,15,9,14,10,10,9,11,9,12,8,10,8, 15,9,11,9,11,4,5,2,2,10,5,8,8, 13,11,10,17,14,10,16,11,9,9,11,9,7, 11,4,7,6,6,4,3,12,10,12,8,9,9, 9,9,12,10,7,11,11,5,4,9,9,11,5, 8,7,3,1,3,17,21,14,11,13,16,8,15, 6,19,12,10,14,12,16,9,6,8,8,2,7, 11,6,5,9,14,6,11,9,8,14,7,10,12, 15,12,9,4,13,9,6,9,7,6,10,8,4, 6,8,11,13,10,13,15,10,12,12,14,8,16, 12,10,8,5,9,10,5,6,7,1,8,3,8, 6,10,5,4,11,7,7,5,7,12,7,14,14, 11,10,4,10,7,9,7,2,4,4,1,0,1, 4,8,3,12,8,9,9,7,9,7,7,7,10, 9,11,4,4,7,4,4,3,7,9,9,13,10, 15,13,13,11,11,13,12,8,12,13,5,6,13, 14,9,5,7,7,7,8,13,7,9,9,5,5, 16,6,11,11,10,11,9,6,6,10,11,7,5, 10,8,6,1,10,8,3,8,6,6,10,5,2, 5,3,2,8,10,10,3,2,10,4,7,4,4, 12,7,5,7,6,6,1,8,3,2,7,6,7, 9,6,5,5,6,4,2,1,6,3,4,5,1, 2,7,7,4,8,7,7,9,9,6,10,9,8, 8,6,4,2,7,6,2,4,3,5,3,4,2, 10,12,4,7,5,4,7,8,7,6,9,5,3, 5,4,5,5,4,5,4,7,6,5,8,4,3, 8,8,6,4,5,7,2,5,1,3,3,5,3, 7,5,2,3,2,2,1,13,16,9,17,10,12, 11,18,18,17,12,14,9,13,11,7,9,5,9, 11,3,4,4,5,7,12,7,8,12,9,6,10, 13,15,9,10,8,8,14,15,6,15,6,10,11, 2,3,0

(a) Let Xbe the number of calls that arrive at the call center in a 10 minute interval. Find the relative frequency (probability) distribution of Xfrom the data collected in October.

(b) Calculate the average number of calls received per 10 minute interval in October.

(c) Randomly occurring telephone calls are often modeled by a Poisson distribution. Calculate the probability distribution of Xassuming a Poisson distribution with mean that you calculated in part (b).

(d) Plot the two probability distributions (a) and (c) together on the same plot. Look- ing at the plot, decide whether our assumption that Xfollows a Poisson distribution is reasonable or not.

Complete the problem in jupyter notebook.