An automated sensor records temperature readings from a process that follows a normal distribution. Initially, the process is set with a mean of 55∘C55^{\circ}\text{C}55∘C and a standard deviation of 4.0∘C4.0^{\circ}\text{C}4.0∘C.
Find the probability that a randomly recorded temperature reading is greater than 62∘C62^{\circ}\text{C}62∘C.
The operator changes the mean to μ\muμ but maintains the standard deviation at 4.0∘C4.0^{\circ}\text{C}4.0∘C. The sensor then records 2 independent temperature readings.
The probability that both of these readings are less than 48∘C48^{\circ}\text{C}48∘C is 0.090.090.09.
Find the value of μ\muμ, giving your answer to 1 decimal place.
The calibration is adjusted again so that the mean is 121212 and the standard deviation is 151515.
The sensor then records 4 independent readings from this distribution.
Find the probability that at least one of these readings is negative.
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.