The cooling system for a quantum processor is monitored during a stability test. The operating temperature, TTT Kelvin, is modelled by a normal distribution with a mean of 84.284.284.2 K.
Sketch the distribution of TTT. Label the mean on your sketch.
The target operating limit for the system is 82.582.582.5 K. The standard deviation of the system's temperature is 1.41.41.4 K.
Find the percentage of time that the system operates below the target limit of 82.582.582.5 K.
The coldest 1.5%1.5\%1.5% of temperature readings trigger an automatic safety shutdown.
Show that the maximum temperature to trigger a safety shutdown, correct to 3 significant figures, is 81.281.281.2 K. Show your working clearly.
Maintenance alerts are issued if a temperature reading ttt falls in a range such that:
P(t<T<82.5)=0.075 P(t < T < 82.5) = 0.075 P(t<T<82.5)=0.075Find the value of ttt, giving your answer to 1 decimal place. Show your working clearly.
390 exam-style questions on OCR (MEI) A Level Maths 2.4 Probability Distributions, covering 2.4.1 Recognise binomial situations, 2.4.2 Probability of success p, 2.4.3 Calculate binomial probabilities, 2.4.4 Mean of the binomial distribution, 2.4.5 Expected frequencies for binomial, 2.4.6 Probability functions and discrete random variables, 2.4.7 Numerical probabilities for a simple distribution, 2.4.8 Normal distribution as a model (A-level only), 2.4.9 Shape of the Normal curve (A-level only), 2.4.10 Linear transformation and standardising (A-level only), 2.4.11 Symmetry and inflection of Normal curve (A-level only), 2.4.12 Calculate probabilities from a Normal distribution (A-level only), 2.4.13 Model with probability distributions, and 2.4 Probability Distributions. Each one has a worked solution and a mark scheme showing where the marks go.