The masses, in milligrams, of three minerals found in 1 tonne of a certain kind of rock are modelled by three independent random variables $P$, $Q$ and $R$, where $P \sim N\left( {46,{\text{ }}{{19}^2}} \right)$, $Q \sim N\left( {53,{\text{ }}{{23}^2}} \right)$ and $R \sim N\left( {25,{\text{ }}{{10}^2}} \right)$. The total value of the minerals found in 1 tonne of rock is modelled by the random variable $V$, where $V = P + Q + 2R$. Use the model to find the probability of finding minerals with a value of at least 93 in a randomly chosen tonne of rock.
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