(i) To draw the cumulative frequency graph, calculate the cumulative frequencies:

• 1 – 20: 10
• 21 – 40: 10 + 32 = 42
• 41 – 50: 42 + 62 = 104
• 51 – 60: 104 + 50 = 154
• 61 – 70: 154 + 28 = 182
• 71 – 90: 182 + 18 = 200

Plot these cumulative frequencies against the upper class boundaries: (20.5, 10), (40.5, 42), (50.5, 104), (60.5, 154), (70.5, 182), (90.5, 200).

(ii) To estimate the number of days when over 30 rooms were occupied, find the cumulative frequency for 30 rooms using linear interpolation between 20 and 40:

Using linear interpolation:

\(10 + \frac{30 - 20.5}{20} \times 32 = 25.2\)

Thus, the cumulative frequency for 30 rooms is approximately 25.2. Therefore, the number of days when over 30 rooms were occupied is \(200 - 25.2 = 174.8\), which rounds to 175 days.

(iii) To find the number of rooms occupied on 75% of the days, calculate 75% of 200 days:

\(0.75 \times 200 = 150\)

Using the cumulative frequency graph, find the number of rooms corresponding to a cumulative frequency of 150. This occurs between 51 and 60 rooms. Using linear interpolation:

\(50.5 + \frac{150 - 104}{50} \times 10 = 59\)

Thus, on 75% of the days, at most 59 rooms were occupied.