3. The heights of 25 students are approximately normally distributed with a mean of $174.5 \mathrm{-cm] $ and a standard deviation of $6.9 \mathrm{-cm} $. b) What is the probability of a student's average height between (4 marks) $172.5$ and $175.8 \mathrm{-cm} $. c) If 200 random samples are drawn from the population, determine (4 marks) how many students have mean height falling below $172 \mathrm{-cm} $. Formulae $P(A \cup B)=P(A)+P(B)-P(A \cap B)$ $P(A \mid B)=\frac{P(A \cap B)}{P(B)} \quad E(X)=\sum x p(x) $ $V(X)=E\left(X^{2} ight)-E(X)^{2} $ $P(X)=e^{-\mu}\left(\frac{\mu^{x}}{x \mid} ight) $ $P(X)={ }^{n} C_{x} p^{x} q^{n-x}$ $z=\frac{x-\mu}{\sigma) $ SP.AS. 15811