Answer:
Roughly a 95% chance.
Step-by-step explanation:
The standard deviation of sample of size 'n' and with a proportion 'p' is given by:
In this case, in a sample of 400 residents with proportion 20%, the standard deviation is:
The upper and lower limits proposed (0.16 and 0.24) are exactly two standard deviations above and below the mean of 0.20. According to the 95% rule, this interval comprehends 95% of all data. Therefore, there is roughly a 95% chance that the resulting sample proportion will be within 0.04 of the true proportion.