To calculate the standard time, we need to account for both the normal time and the allowances. The formula for standard time is:
\[
{Standard Time} = {Normal Time} \times (1 + {Allowance})
\]
Here, the normal time for manufacturing a product is 5 minutes.
- The worker is allowed 30 minutes of personal time in a normal 8-hour shift. The total shift time is 480 minutes (8 hours), and the allowance is \( \frac{30}{480} = 0.0625 \) or 6.25%.
Now, calculate the standard time:
\[
{Standard Time} = 5 \times (1 + 0.0625) = 5 \times 1.0625 = 5.3125 { minutes}.
\]
To convert this to seconds:
\[
5.3125 \times 60 = 318.75 { seconds}.
\]
Thus, the standard time lies between 315 and 325 seconds.