6. Normal Distribution and Continuous Random Variables

The arrival times of the bus Alex takes to work follow a normal distribution, with $\mu =12\min$ after the scheduled arrival rime & $\sigma =3\min$. If the bus is scheduled to arrive at Alex's work 10 min before opening, what is the probability that Alex arrives on time (i.e. the bus is less than 10 min late)?

The heights of adult women are approximately normally distributed with a mean of $160\mathrm{cm}$ and a standard deviation of $7\mathrm{cm}$. Find the height $x$ such that $5\%$ of women are shorter than $x$.