Final answer:
The statement regarding normally distributed data that is NOT true is that approximately 68% of the data lies within two standard deviations of the median; for a normal distribution, this percentage is within one standard deviation of the mean.
Step-by-step explanation:
The statement that is NOT true for normally distributed data is A: "Approximately 68% of all the data lies within two standard deviations of the median". In a normal distribution, approximately 68% of the data lies within one standard deviation of the mean, not two. It is also important to clarify that for normally distributed data, the mean, median, and mode are all the same point, and about 95% of the data lies within two standard deviations of the mean. Statement B is true as the area under the curve of a normal distribution is always 1 regardless of the mean and standard deviation. Statement C is true because almost all the data (over 99%) lies within three standard deviations of the mean. Statement D is true because in a normal distribution, the mean and median are the same due to the symmetrical nature of the distribution.