Question

Two resistors, with resistances R1and R 2 , are connected in series. R1 is normally distributed with mean 65Ω and standard deviation 10Ω, and R2 is normally distributed with mean75Ω and standard deviation 5Ω. What is the probability that R 2 >R 1

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Answer 1

To find the probability that R2 is greater than R1 in a series circuit, standardize the values using the Z-score formula and refer to the standard normal distribution table or use statistical software to find the probability.

Step-by-step explanation:

To find the probability that R2 is greater than R1 in a series circuit, we need to determine the probability distribution of the two resistances. Since R1 is normally distributed with a mean of 65Ω and standard deviation of 10Ω, and R2 is normally distributed with a mean of 75Ω and standard deviation of 5Ω, we can use the properties of normal distributions to calculate the probability.

First, let's standardize the values using the Z-score formula: Z1 = (R1 - mean1) / standard deviation1 and Z2 = (R2 - mean2) / standard deviation2.

Next, we can use the standardized values to find the probability that Z2 is greater than Z1 by referring to the standard normal distribution table or using a statistical software. This probability represents the likelihood that R2 is greater than R1 in the series circuit.