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.
616 exam-style questions on Edexcel A Level Maths The Normal Distribution, covering 3.1 The Normal Distribution, 3.2 Finding Probabilities for Normal Distributions, 3.3 The Inverse Normal Distribution Function, 3.4 The Standard Normal Distribution, 3.5 Finding the mean and standard deviation, 3.6 Approximating a Binomial Distribution, and 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.