4. A music website is visited by an average of 30 different people per hour on a weekday evening. The site's designer believes that the number of visitors to the site per hour can be modelled by a Poisson distribution.

1. State the conditions necessary for a Poisson distribution to be applicable and comment on their validity in this case. Assuming that the number of visitors does follow a Poisson distribution, find the probability that there will be
2. less than two visitors in a 10 -minute interval,
3. at least ten visitors in a 15-minute interval.
4. Using a suitable approximation, find the probability of the site being visited by more than 100 people between 6 pm and 9 pm on a Thursday evening.
   (5 marks)