4.A small startup tech company has 4 customer service telephone lines. Let denote

the number of phone lines in use at any given time. Suppose that the probability distribution of is as follows:

=0 1 2 3 4

()= 0.10 0.16 a 0.31 0.22

a.)Determine the value of if the data above represent a discrete probability

distribution.

b.) Calculate and interpret the expected value of .

c.) Calculate the standard deviation of .