A normal distribution with a mean of 50 and a standard deviation of 4 describes a symmetric, bell-shaped curve where most of the observations cluster around the mean. In this scenario, the mean (or average) value is 50, indicating the center of the distribution.
The standard deviation of 4 indicates how much the values vary around the mean. A smaller standard deviation would mean that the data points are closer to the mean, while a larger standard deviation would suggest that the data points are more spread out. Here, 68% of the values fall within one standard deviation (46 to 54), and about 95% fall within two standard deviations (42 to 58). This characteristic is fundamental in statistics, as it helps in understanding how data behaves in various scenarios.