The data given below show the number of overtime hours worked in one week per employee. Use the data to complete parts (a) and (b).
Overtime hours
Employees
0
8
1
2
3
4
6 16
(a) Construct a probability distribution
(b) Graph the probability distribution using a histogram and describe its shape.
(a) Construct the probability distribution by completing the table below.
\[
\begin{array}{c}
x \\
P(x)
\end{array}
\]
3
4
5
6
(Round to three decimal places as needed.)

Step 1 ：The data given in the question is not clear. It seems like the number of overtime hours are 0, 1, 2, 3, 4, 6 and 16. But the number of employees for each overtime hour is not given. Assuming that the number of employees for each overtime hour is 1, we can calculate the probability for each overtime hour.

Step 2 ：To construct a probability distribution, we need to calculate the probability of each unique value in the data. The probability of a particular value is calculated by dividing the frequency of that value by the total number of values.

Step 3 ：The Python code has calculated the probability distribution for the given data. The probability for each overtime hour is 0.142857, which is the result of dividing the number of employees (1) by the total number of employees (7).

Step 4 ：However, the question asks for the probability distribution for the overtime hours 3, 4, 5, and 6. We can see from the calculated probability distribution that the probabilities for the overtime hours 3 and 4 are 0.142857. The overtime hour 5 is not in the data, so its probability is 0. The probability for the overtime hour 6 is also 0.142857.

Step 5 ：Final Answer: The probability distribution for the overtime hours 3, 4, 5, and 6 is as follows: For overtime hour 3, \(P(3) = \boxed{0.143}\) For overtime hour 4, \(P(4) = \boxed{0.143}\) For overtime hour 5, \(P(5) = \boxed{0}\) For overtime hour 6, \(P(6) = \boxed{0.143}\)