Question: The time of failure for a continuous operation monitoring device of air quality has a uniform distribution over a 24 hour day:

a. If a failure occurs on a day when daylight is between 5:55 and 7:38 p.m., what is the probability that the failure will occur during daylight hours?

b. If the device is in secondary mode from 10pm to 5am, what is the probability that if a failure occurs, it will happen during secondary mode?

c. If the device has a self-checking computer chip that determines if the device is operational every hour on the hour, what is the probability that a failure will be detected within ten minutes of its occurrence?

d. If the device has a self-checking computer chip that determines if the device is operational every hour on the hour, what is the probability that it will take at least 30 minutes to detect that a failure ahs occurred?