7. The distances travelled to work, \(D \mathrm {~km}\), by the employees at a large company are normally distributed with \(D \sim \mathrm {~N} \left( 30,8 ^ { 2 } \right)\).
- Find the probability that a randomly selected employee has a journey to work of more than 20 km .
- Find the upper quartile, \(Q _ { 3 }\), of \(D\).
- Write down the lower quartile, \(Q _ { 1 }\), of \(D\).
An outlier is defined as any value of \(D\) such that \(D < h\) or \(D > k\) where
$$h = Q _ { 1 } - 1.5 \times \left( Q _ { 3 } - Q _ { 1 } \right) \quad \text { and } \quad k = Q _ { 3 } + 1.5 \times \left( Q _ { 3 } - Q _ { 1 } \right)$$
- Find the value of \(h\) and the value of \(k\).
An employee is selected at random.
- Find the probability that the distance travelled to work by this employee is an outlier.