2. Sunita and Shelley talk to one another once a week on the telephone. Over many weeks they recorded, to the nearest minute, the number of minutes spent in conversation on each occasion. The following table summarises their results.
| Time | | (to the nearest minute) |
| |
| \(5 - 9\) | 2 |
| \(10 - 14\) | 9 |
| \(15 - 19\) | 20 |
| \(20 - 24\) | 13 |
| \(25 - 29\) | 8 |
| \(30 - 34\) | 3 |
Two of the conversations were chosen at random.
- Find the probability that both of them were longer than 24.5 minutes.
The mid-point of each class was represented by \(x\) and its corresponding frequency by \(f\), giving \(\Sigma f x = 1060\).
- Calculate an estimate of the mean time spent on their conversations.
During the following 25 weeks they monitored their weekly conversations and found that at the end of the 80 weeks their overall mean length of conversation was 21 minutes.
- Find the mean time spent in conversation during these 25 weeks.
- Comment on these two mean values.