Final answer:
The probability that the mean amount of water in the 16 bottles is within 5 mL of the population mean is 50%.
Step-by-step explanation:
To find the probability that the mean amount of water in the 16 bottles is within 5 mL of the population mean, we need to calculate the z-score for the given values. The z-score formula is z = (x - µ) / (σ / sqrt(n)), where x is the sample mean, µ is the population mean, σ is the population standard deviation, and n is the sample size.
Plugging in the values, we have z = (505 - 505) / (10 / sqrt(16)) = 0. The z-score of 0 represents the mean of the sample, which is equal to the population mean. Therefore, the probability is 50%, as half the values lie below the mean in a normal distribution.