3. The parking times, \(t\) hours, for cars in a car park are summarised below.
| Time (t hours) | Frequency (f) | Time midpoint (m) |
| \(0 \leqslant t < 1\) | 10 | 0.5 |
| \(1 \leqslant t < 2\) | 18 | 1.5 |
| \(2 \leqslant t < 4\) | 15 | 3 |
| \(4 \leqslant t < 6\) | 12 | 5 |
| \(6 \leqslant t < 12\) | 5 | 9 |
$$\text { (You may use } \sum \mathrm { fm } = 182 \text { and } \sum \mathrm { fm } ^ { 2 } = 883 \text { ) }$$
A histogram is drawn to represent these data.
The bar representing the time \(1 \leqslant t < 2\) has a width of 1.5 cm and a height of 6 cm .
- Calculate the width and the height of the bar representing the time \(4 \leqslant t < 6\)
- Use linear interpolation to estimate the median parking time for the cars in the car park.
- Estimate the mean and the standard deviation of the parking time for the cars in the car park.
- Describe, giving a reason, the skewness of the data.
One of these cars is selected at random.
- Estimate the probability that this car is parked for more than 75 minutes.