A store sells bags of candy with an average weight of 250 grams per bag. The actual weight of each bag follows a normal distribution with a standard deviation of 25 grams. What is the approximate probability that a randomly selected bag weighs between 225 and 275 grams?
To find the probability that a randomly selected bag weighs between 225 and 275 grams, we'll use the empirical rule for normal distributions. According to this rule, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.

In this case, the mean is 250 grams, and one standard deviation is 25 grams. The range of 225 to 275 grams represents a range of plus or minus one standard deviation from the mean:

Lower limit = Mean - 1 * Standard deviation
                    = 250 - 25
                    = 225 grams

Upper limit = Mean + 1 * Standard deviation
                    = 250 + 25
                    = 275 grams

Since our desired range falls within one standard deviation of the mean, we can use the empirical rule to approximate the probability:

Probability = Approximately 68%

So, there's approximately a 68% chance that a randomly selected bag of candy weighs between 225 and 275 grams.