A high-precision monitoring system for a data center records hardware interrupts occurring at an average rate of 2.8 per hour.
Find the probability that the system records more than 45 interrupts in a 15-hour window.
The system uses a temporary cache to store interrupt data for 12-hour cycles. Determine the minimum integer capacity C C\,C of the cache such that the probability of the number of interrupts exceeding the capacity in a single cycle is less than 0.02.
After a firmware update, the system is monitored for 50 hours. During this time, a total of 165 interrupts are recorded. Using a suitable approximation and a 5% level of significance, test whether there is evidence that the average rate of system interrupts has increased. State your hypotheses clearly.
