1. **Problem 1:** Find the probability that a child picked at random has a height greater than 104cm. Given: $X=104$, $\mu=110$, $\sigma=5$ Formula: Use the standard normal distribution $Z=\frac{X-\mu}{\sigma}$. Calculate $Z$: $$Z=\frac{104-110}{5}=\frac{-6}{5}=-1.2$$ Find $P(X>104)=P(Z>-1.2)$. Using standard normal tables or symmetry: $$P(Z>-1.2)=1-P(Z\leq -1.2)=1-0.1151=0.8849$$ So, the probability is approximately 0.8849. 2. **Problem 2:** Find the probability that the height of a child picked at random is less than 116cm. Given: $X_1=116$, $\mu=110$, $\sigma=5$ Calculate $Z$: $$Z=\frac{116-110}{5}=\frac{6}{5}=1.2$$ Find $P(X<116)=P(Z<1.2)$. From standard normal tables: $$P(Z<1.2)=0.8849$$ So, the probability is approximately 0.8849. 3. **Problem 3:** Find how many children are between 98cm and 122cm. Given: $X=98$, $X_2=122$, $\mu=110$, $\sigma=5$ Calculate $Z$ values: $$Z_1=\frac{98-110}{5}=\frac{-12}{5}=-2.4$$ $$Z_2=\frac{122-110}{5}=\frac{12}{5}=2.4$$ Find $P(98 X_c) = 0.15$. Find $Z_c$ such that $P(Z > Z_c) = 0.15$. From standard normal tables, $Z_c \approx 1.04$. Calculate $X_c$: $$X_c=\mu + Z_c \times \sigma = 110 + 1.04 \times 5 = 110 + 5.2 = 115.2$$ Number of children: $$500 \times 0.15 = 75$$ **Final answers:** 1. Probability height $>$ 104cm is approximately 0.8849. 2. Probability height $<$ 116cm is approximately 0.8849. 3. Number of children between 98cm and 122cm is approximately 492. 4. Number of children in the upper 15% is 75.