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?

Answer:

Step 1 of 2:

(a)

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,

=

=

Where .

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

Therefore .