1. **Stating the problem:** We want to find the formula for the number $N$ of employees needed to perform an activity that takes time $t$ per occurrence, is performed $n$ times per work day, with a capacity utilisation of $a$ percent, and a total work day duration $T$. 2. **Understanding the variables:** - $t$: time per activity - $n$: number of times activity is performed per day - $a$: capacity utilisation in percent - $T$: total duration of the work day - $N$: number of employees needed 3. **Key concept:** The total time required for the activity per day is $n \times t$. 4. **Capacity utilisation means:** The employees are only effectively working $a\%$ of their time, so the available effective work time per employee is $\frac{a}{100} \times T$. 5. **Formula for number of employees:** $$N = \frac{\text{total required time}}{\text{effective time per employee}} = \frac{n \times t}{\frac{a}{100} \times T} = \frac{n \times t}{aT/100} = \frac{n \times t \times 100}{a \times T}$$ 6. **Simplify and confirm:** $$N = \frac{n \cdot t \cdot 100}{T \cdot a}$$ 7. **Conclusion:** The correct formula among the options is: $$N = \frac{n \cdot t \cdot 100}{T \cdot a}$$ This matches the fourth option. **Final answer:** $N = \frac{n \cdot t \cdot 100}{T \cdot a}$