Final answer:
Yes, it is true that rough percentile estimates can be made with a normal distribution if the mean and standard deviation are known. This is due to the characteristics of the normal distribution as defined by the Empirical Rule and is supported by the central limit theorem.
Step-by-step explanation:
True. If one assumes a normal distribution and knows the mean and standard deviation, one can indeed make rough percentile estimates. This is because a normal distribution has specific characteristics that allow for the prediction of where percentiles lie. For a data set with a distribution that is bell-shaped and symmetric (normal distribution), it's known that approximately 68 percent of the data falls within one standard deviation of the mean, about 95 percent within two standard deviations, and over 99 percent within three standard deviations. These figures are part of the Empirical Rule which is particularly helpful in making these percentile estimations.
Additionally, the central limit theorem supports the idea that the sampling distribution of the means approaches a normal distribution as the sample size gets larger, in effect allowing one to create confidence intervals and make estimations regarding population parameters based on sample statistics.