To calculate the probability that a value is within one standard deviation, first determine the z-scores for one standard deviation above and below the mean using the formula z = (x - m) / sigma. Once the z-scores are calculated, use the standard normal distribution table to find the probabilities associated with these z-scores. The probability of a value falling within one standard deviation can be found by subtracting the probability of the lower z-score from the probability of the upper z-score. This approach provides the required probability for values within one standard deviation of the mean. Understanding these calculations is essential for solving probability problems in statistics.