Two resistors, with resistances R1 and R2, are connected in series. R1 is normally distributed with mean 100 Ω and standard deviation 5 Ω, and R2 is normally distributed with mean 120 Ω and standard deviation 10 Ω.
a. What is the probability that R2 > R1?
b. What is the probability that R2 exceeds R1 by more than 30 Ω?
Step 1 of 2:
In this question, we are asked to find the probability that
is normally distributed with mean 100 and standard deviation .
is normally distributed with mean 120 and standard deviation .
Both resistor are connected in series.
We need to find the we can rewrite as,
Since both and are independent random variable and normally distributed, we can do the linear combinations of mean and standard deviations.
Since is a linear combination of independent normal random variable, is also normally distributed.
Now we will calculate the z-score, to find
The z-score of 0 is z =
From the z table, the area to the left of is 0.0375.
The area to the right of is