A particular fruit's weights are normally distributed, with a mean of 415 grams and a standard deviation of 31 grams. The heaviest 4% of fruits weigh more than how many grams?

Answer 1

The heaviest 4% of the fruits corresponds to the 96th percentile.

First find the z-score that corresponds to the 96th percentile, which is 1.751 as P(Z < 1.751) = 0.96.

standardized z score z = (x - mean)/standard deviation, where x = fruit weight

1.751 = (x - 415)/31

solve for x to get fruit weight for 96th percentile (or lower bound of heaviest 4% of fruit)