3 A website owner finds that, on average, his website receives 0.3 hits per minute. He believes that the number of hits per minute follows a Poisson distribution.
- Assume that the owner is correct.
- Find the probability that there will be at least 4 hits during a 10-minute period.
- Use a suitable approximating distribution to find the probability that there will be fewer than 40 hits during a 3-hour period.
A friend agrees that the website receives, on average, 0.3 hits per minute. However, she notices that the number of hits during the day-time ( 9.00 am to 9.00 pm ) is usually about twice the number of hits during the night-time ( 9.00 pm to 9.00 am ).
- Explain why this fact contradicts the owner's belief that the number of hits per minute follows a Poisson distribution.
- Specify separate Poisson distributions that might be suitable models for the number of hits during the day-time and during the night-time.