Problem
The weight of oranges growing in an orchard is normally distributed with a mean weight of \( 7.5 \mathrm{oz} \). and a standard deviation of \( 1.5 \mathrm{oz} \). Using the empirical rule, determine what interval would represent weights of the middle \( 95 \% \) of all oranges from this orchard.
Solution
Step 1 ：\(95\%\) of the data lies within \(\pm 2\) standard deviations of the mean.
Step 2 ：Lower limit: \(7.5 - 2(1.5) = 4.5\) oz
Step 3 ：Upper limit: \(7.5 + 2(1.5) = 10.5\) oz
