A high-precision centrifuge is used in a chemical refinement process. The process involves two stages of separation.
The time, SSS minutes, taken to complete the first separation stage is modelled by a normal distribution with mean 112.5 minutes and standard deviation 14.8 minutes.
Use standardisation to find the proportion of cycles that take less than 135.0 minutes to complete the first separation stage.
Only the most efficient 12% of cycles (those with the shortest completion times) from the first separation stage are passed through to a second refinement stage.
Use standardisation to find the maximum time a cycle can take in the first separation stage if it is to be passed through to the second refinement stage.
The time, TTT minutes, for a cycle in the second refinement stage is modelled by a normal distribution with mean μ\muμ and standard deviation σ\sigmaσ.
Given that P(μ−10.4<T<μ+10.4)=0.82P(\mu - 10.4 < T < \mu + 10.4) = 0.82P(μ−10.4<T<μ+10.4)=0.82
Find P(T>μ−5.2∣T>μ−10.4)P(T > \mu - 5.2 \mid T > \mu - 10.4)P(T>μ−5.2∣T>μ−10.4)