Mathematics: Two resistors, with resistances R1 and R2, are connected in series. R1 is normally distributed with mean 100 ohms and standard deviation 5 ohms, and R2 is normally distributed with mean 120 ohms and standard deviation 10 ohms. Assume that the resistors are independent. Compute P (R subscript 2 greater than R subscript 1 ). Round your answer to four decimal places.

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Two resistors, with resistances R1 and R2, are

debramknoxx

20.01.2022

The probability that R2 is bigger than R1 is P=0.9633.

Step-by-step explanation:

We need to compute the probability that R2 is bigger than R1:

P(R_2R_1)

To do this, we define a new variable Das the difference between the two resistances:

D=R_2-R_1

Then,

P(R_2R_1)=P(R_2-R_10)=P(D0)

As R1 and R2 are normal random variables, the properties of D are:

$\mu_D=\mu_{R2}-\mu_{R1}=120-100=20\\\\\sigma_D=\sqrt{\sigma_{R2}^2+\sigma_{R1}^2}=\sqrt{10^2+5^2}=\sqrt{100+25}=\sqrt{125}=11.18$

Then, we can calculate the z-value for D=0

$z=\frac{x-\mu}{\sigma} =\frac{0-20}{11.18}=\frac{-20}{11.18}= -1.79$

P(D0)=P(z-1.79)=0.9633

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