Probability of a Gaussian random variable

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Hi have the following problem... I have a tank represented with a Gaussian random variable: $X\sim N(6;0.25)$, the request:

  • Check that the sum of two independent measures is greater than 10 meters

How can I check my solution? Thank you

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Hint: The sum of two independent measures is still a Gaussian

$Z=X+Y \sim N(12; 0.5)$