The incomplete table provided is a discrete random variable X's probability distribution, where x is the number of community service projects members of an Alpha Sigma Chi sorority participated in within the past 12 months.Answer the following:

a) Determine the value that is missing in the table.

b) Explain the meaning of P(x=3) as it applies to the context of this problem.

c) Determine the value of P(x 3).

d) Find the probability that x is at most 4.

e) Expand the table provided and use Excel to calculate the mean (expected value) and standard deviation of this probability distribution.Label the columns in your expanded table.

i. Mean:

ii. Standard Deviation:

TABLE

x P(X=x)

1 0.03

2 0.11

3 0.21

4 ______

5 0.22

6 0.15