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.
228 exam-style questions on CCEA A Level Maths 4.5.1 Statistical distributions (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.