Median, percentile and quartiles of waiting times from a cumulative frequency curve and a box plot, with an outlier boundary

On one day, a bank recorded how long each of its \(200\) customers waited, in minutes, before being served. The cumulative frequency curve below summarises these waiting times.

1. Use the curve to find the median waiting time.[2]
2. Find how many customers waited for a time that differs from the median by no more than \(4\) minutes.[3]

Exactly \(10\%\) of these customers waited longer than \(k\) minutes.

3. Find the value of \(k\).[3]

The same waiting times are summarised in the box-and-whisker diagram below, which shows the shortest time, the lower quartile, the median, the upper quartile and the longest time.

4. Write down the value of \(b\).[1]
5. 1. Find the value of \(a\).
   2. Hence, find the interquartile range of the waiting times.[4]

A waiting time is classed as an outlier if it is less than \(p\) minutes, where \(p\) is \(1.5\) interquartile ranges below the lower quartile.

6. Find the value of \(p\).[2]