1. **Problem:** Find the percentage of students with weights between 123.2 kg and 138.4 kg, given weights are normally distributed with mean $\mu=134.6$ kg and standard deviation $\sigma=3.8$ kg. 2. **Formula:** Use the standard normal variable $Z=\frac{X-\mu}{\sigma}$ to convert weights to $Z$-scores. 3. **Calculate $Z$-scores:** $$Z_1=\frac{123.2-134.6}{3.8}=\frac{-11.4}{3.8}=-3$$ $$Z_2=\frac{138.4-134.6}{3.8}=\frac{3.8}{3.8}=1$$ 4. **Interpretation:** We want $P(123.2 < X < 138.4) = P(-3 < Z < 1)$. 5. **Use standard normal table or calculator:** $$P(Z<1)=0.8413$$ $$P(Z<-3)=0.0013$$ 6. **Calculate probability:** $$P(-3