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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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Answer:

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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