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2 June, 03:53

Two resistors, with resistances R1 and R2, are connected in series. R1 is normally distributed with mean 65 and standard deviation 10, and R2 is normally distributed with mean 75 and standard deviation 5.

a. What is the probability that R2 > R1?

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  1. 2 June, 07:09
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    n this question, we are asked to find the probability that

    R1 is normally distributed with mean 65 and standard deviation 10

    R2 is normally distributed with mean 75 and standard deviation 5

    Both resistor are connected in series.

    We need to find P (R2>R1)

    the we can re write as,

    P (R2>R1) = P (R2-R1>R1-R1)

    P (R2>R1) = P (R2-R1>0)

    P (R2>R1) = P (R>0)

    Where;

    R = R2 - R1

    Since both and are independent random variable and normally distributed, we can do the linear combinations of mean and standard deviations.

    u = u2-u1

    u = 75 - 65 = 10ohm

    sd = √sd1² + sd2²

    sd = √10²+5²

    sd = √100+25 = 11.18ohm

    Now we will calculate the z-score, to find P (R>0)

    Z = (X - u) / sd

    the z score of 0 is

    z = 0 - 10/11.18

    z = - 0.89
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