A small start up tech company has 4 customer service telephone lines. Let xdenote the number of phone lines in use at any given time. Suppose that the probability distribution of x is as follows:

x Px

0 0.10

1 0.16

2 a

3 0.31

4 0.22

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

b.) Calculate and interpret the expected value of x.

c.) Calculate the standard deviation of x.