Question: The time to failure for a continuousoperation 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 a.m. 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 10 p.m. to 5 a.m., 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 whether the device is operational every hour on the hour, what is the probability that a failure will be detected within 10 minutes of its occurrence?
d. If the device has a self-checking computer chip that determines whether the device is operational every hour on the hour, what is the probability that it will take at least 40 minutes to detect that a failure has occurred?