1. **Problem statement:** We are given a normally distributed height of students with mean $\mu=125$ cm and standard deviation $\sigma=3.5$ cm. We want to find the percentage of students with height: - Greater than 135 cm - Less than 128 cm - Between 115 cm and 130 cm 2. **Formula and rules:** For a normal distribution, we use the standard normal variable $Z=\frac{X-\mu}{\sigma}$ to find probabilities. We use standard normal distribution tables or a calculator to find $P(Z \leq z)$. 3. **Calculate $Z$ values:** - For $X=135$: $$Z=\frac{135-125}{3.5}=\frac{10}{3.5}=2.857$$ - For $X=128$: $$Z=\frac{128-125}{3.5}=\frac{3}{3.5}=0.857$$ - For $X=115$: $$Z=\frac{115-125}{3.5}=\frac{-10}{3.5}=-2.857$$ - For $X=130$: $$Z=\frac{130-125}{3.5}=\frac{5}{3.5}=1.429$$ 4. **Find probabilities using standard normal distribution:** - $P(X>135)=P(Z>2.857)=1-P(Z\leq 2.857)\approx 1-0.9979=0.0021$ or 0.21% - $P(X<128)=P(Z<0.857)\approx 0.804$ or 80.4% - $P(115