Given the table, we have:
Add all probabilities
0.366 + 0.427 + 0.180 + 0.027 = 1
The table describes a probability distribution because all probabilities are between 0 and 1, and the sum of probabilities is equal to 1.
For mean:

For standard deviation:

Simplify:

Answer:
Yes, the table shows a probability distribution
mean = 0.868
standard deviation = 0.798