Step 1 :First, we need to find the total number of employees. We add up the number of employees for each overtime hour: \(3+1+2+8+10+29+55+46+26+6 = 156\).
Step 2 :Next, we calculate the probability for each overtime hour by dividing the number of employees who worked that many hours by the total number of employees. For example, the probability for 0 hours is \(\frac{3}{156} = 0.019\) (rounded to three decimal places).
Step 3 :We repeat this process for each overtime hour to complete the probability distribution table.
Step 4 :For the histogram, we use the overtime hours as the x-axis and the probabilities as the y-axis. Each bar represents an overtime hour, and its height is the corresponding probability.
Step 5 :The shape of the histogram can be described after it is drawn. If the bars decrease in height as the overtime hours increase, the distribution is right-skewed. If the bars increase in height as the overtime hours increase, the distribution is left-skewed. If the bars form a bell shape, the distribution is symmetric.