A small start up tech company has 4 customer service telephone lines. Letdenote the number of phone lines in use at any given time. Suppose that the probability distribution of is as follows: (10 points) 0

0.10

1

0.16

2

a

3

0.31

4

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 .