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.