A scientific research team uses two types of atmospheric sensors. The operational duration of each sensor is normally distributed. A Type-A sensor has a mean duration of 180 hours and a standard deviation of 8 hours. A Type-B sensor has a mean duration of 42 hours and a standard deviation of 3 hours.
Determine the probability that the duration of a single Type-A sensor exceeds the combined duration of four randomly selected Type-B sensors.
Find the probability that the duration of one Type-A sensor is less than four times the duration of a single, randomly selected Type-B sensor.
79 exam-style questions on OCR (MEI) A Level Maths 2.4.8 Normal distribution as a model (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.