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Three resistors, with resistances $R_{1},R_{2}$, and $R_{3}$ are connected in series, $R_{1}$ is normally distributed with a mean of $110Ω$ and a standard deviation of $15Ω,R_{2}$ is normally distributed with a mean of $135Ω$ and a standard deviation of $12Ω$, and $R_{3}$ is normally distributed with a mean of $120Ω$ and a standard deviation of $16Ω$. What is the probability that total resistance $(R_{1}+R_{2}+R_{3})$ exceeds $400Ω$ ?

given:

Here, we are given that R1 follows a normal distribution with a mean of 110 and a standard distribution of 15. So, using standard notation we can write, R1 ~ N(110, 15^2)

Similarly, we can write,

R2 ~ N(135, 12^2)

R3 ~ N(120, 16^2)

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