In a manufacturing facility for precision sensors, the probability of a sensor having a calibration error is p=0.12p = 0.12p=0.12. Errors occur independently in each sensor.
Find the probability that in a random sample of 25 sensors, there will be
(i) exactly 4 sensors with a calibration error,
(ii) at least 6 sensors with a calibration error.
In a large batch of 600 sensors, use a suitable approximation to find the probability that the number of sensors with calibration errors is more than 80.
