Final Answers:
1. The median of the distribution is 58.
2. The lower limit for the highest 16% of the data is approximately 72.
Step-by-step explanation:
To find the median of a normal distribution, the median is the same as the mean in a perfectly symmetrical distribution. In a normal distribution, the mean is also the midpoint. Since 40 and 76 are three standard deviations from the mean in both directions, and it's known that three standard deviations cover around 99.7% of the data, the difference between the mean and 76 would be three standard deviations. Therefore, the mean is (76 + 40) / 2 = 58, and hence, the median is also 58.
To determine the lower limit for the highest 16% of the data, note that the remaining 84% (100% - 16% = 84%) would be divided evenly on both sides of the mean in a symmetric distribution. Utilizing the empirical rule, approximately 68% of the data falls within one standard deviation from the mean. So, if we move three standard deviations away from the mean (as 68% + 16% = 84%), the lower limit is 76, which is three standard deviations above the mean.
This concludes that the median of the distribution is 58, and the lower limit for the highest 16% of the data is approximately 72.