In the following probability distribution, the random variable $\mathrm{x}$ represents the number of activities a parent of a 6 th- to 8 th-grade student is involved in. Complete parts (a) through (f) below. \begin{tabular}{c|c|c|c|c|c} $\mathbf{x}$ & 0 & 1 & 2 & 3 & 4 \\ \hline $\mathbf{P}(\mathbf{x})$ & 0.079 & 0.228 & 0.145 & 0.156 & 0.392 \end{tabular} (c) Compute and interpret the mean of the random variable $\mathrm{x}$. The mean is activities. (Type an integer or a decimal. Do not round.)

Step 1 ：The mean of a probability distribution is calculated by multiplying each possible outcome by its probability and then summing these products. In this case, we need to multiply each value of x (number of activities) by its corresponding probability and then sum these products to get the mean.

Step 2 ：Let's denote the number of activities as x and their corresponding probabilities as P(x). The values of x are [0, 1, 2, 3, 4] and the corresponding probabilities are [0.079, 0.228, 0.145, 0.156, 0.392].

Step 3 ：We calculate the mean by multiplying each x value by its corresponding probability and summing these products: \(0*0.079 + 1*0.228 + 2*0.145 + 3*0.156 + 4*0.392\).

Step 4 ：The mean of the random variable x is approximately 2.554.

Step 5 ：Final Answer: The mean of the random variable \(x\) is \(\boxed{2.554}\). This means that on average, a parent of a 6th- to 8th-grade student is involved in approximately 2.554 activities.