$35 \%$ of employees judge their peers by the cleanliness of their workspaces. You randomly select 8 employees and ask them whether they judge their peers by the cleanliness of their workspaces. The random variable represents the number of employees who judge their peers by the cleanliness of their workspaces. Complete parts (a) through (c) below. (a) Construct a binomial distribution using $n=8$ and $p=0.35$. \begin{tabular}{|c|c|} \hline $\mathbf{x}$ & $\mathbf{P}(\mathbf{x})$ \\ \hline 0 & $\square$ \\ \hline 1 & $\square$ \\ \hline 2 & $\square$ \\ \hline 3 & $\square$ \\ \hline 4 & $\square$ \\ \hline 5 & $\square$ \\ \hline 6 & $\square$ \\ \hline 7 & $\square$ \\ \hline 8 & $\square$ \\ \hline \end{tabular} (Type integers or decimals rounded to four decimal places as needed.)

Step 1 ：Construct a binomial distribution using \( n=8 \) and \( p=0.35 \)

Step 2 ：Calculate the probability of each possible number of employees judging their peers by the cleanliness of their workspaces, from 0 to 8

Step 3 ：Use the binomial probability formula: \( P(x) = \binom{n}{x} p^x (1-p)^{n-x} \)

Step 4 ：Calculate the binomial coefficient \( \binom{n}{x} \) as \( \frac{n!}{x!(n-x)!} \)

Step 5 ：Calculate the probabilities for \( x \) ranging from 0 to 8

Step 6 ：Final Answer: \begin{tabular}{|c|c|} \hline \(\mathbf{x}\) & \(\mathbf{P}(\mathbf{x})\) \\ \hline 0 & \boxed{0.0319} \\ \hline 1 & \boxed{0.1373} \\ \hline 2 & \boxed{0.2587} \\ \hline 3 & \boxed{0.2786} \\ \hline 4 & \boxed{0.1875} \\ \hline 5 & \boxed{0.0808} \\ \hline 6 & \boxed{0.0217} \\ \hline 7 & \boxed{0.0033} \\ \hline 8 & \boxed{0.0002} \\ \hline \end{tabular}