A particular fruit's weights are normally distributed, with a mean of 767 grams and a standard deviation of 15 grams. The heaviest 16% of fruits weigh more than how many grams?

Answer 1

By the Empirical Rule we know that approximately 68% of a particular fruit's weights will fall within one standard deviation of the mean. Since the mean is 767 grams and the standard deviation is 15 grams, we know by the Empirical Rule that 68% of a particular fruit's weights will fall between 767 grams - 15 grams = 752 grams and 767 grams + 15 grams = 782 grams and that 32% of a particular fruit's weights will fall outside of this range. From the preceding facts and from the symmetry of the normal distribution we finally have that the heaviest 16% of these particular fruits will weigh more than 782 grams.