To find the standard time for the activity, we use the following formula:

$\text{Standard Time} = \text{Observed Time} \times \left( \frac{\text{Performance Rating}}{100} \right) \times \left( 1 + \text{Allowance Factor} \right)$

Where:

• Observed Time = 15 minutes
• Performance Rating = 97% = 0.97
• Fatigue Allowance = 5% = 0.05
• Special Allowances = 2% = 0.02

First, we calculate the total allowance factor:

$\text{Allowance Factor} = 5\% + 2\% = 7\% = 0.07$

Now, we can calculate the standard time:

$\text{Standard Time} = 15 \times 0.97 \times (1 + 0.07)$ $\text{Standard Time} = 15 \times 0.97 \times 1.07$ $\text{Standard Time} = 15 \times 1.0389 = 15.5835 \text{ minutes}$

So, the standard time for the activity is 15.58 minutes.

Would you like more details on the calculation? Let me know if you have any questions.

Here are some related questions for further exploration:

1. How does the performance rating impact the standard time?
2. What is the purpose of adding allowances to the observed time?
3. How would the standard time change if the observed time were different?
4. How do fatigue and special allowances affect overall productivity?
5. What is the difference between a performance rating and a normal time?

Tip: Always check the units when performing calculations involving percentages to ensure consistency in the final result.