A particular fruit's weights are normally distributed, with a mean of 221 grams and a standard deviation of 12 grams. The heaviest 13% of fruits weigh more than how many grams?

Answer 1

use z-transformation to solve this problem.

z = (x - mean)/standard deviation, where

x = fruit weight, mean = 221 and SD = 12

so:

z = (x - 221)/12

so

z* 12 + 221 = x

Heaviest 13% of fruits would be above the 87th percentile.

Find z-score that corresponds to 87th percentile (cumulative probability of 0.87)

substitute that value for z in the above equation and solve for x.