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Two resistors, with resistances R1 and R2, are connected

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Problem 21E Chapter 4.5

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

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Problem 21E

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-by-Step Solution:

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 .

Step 2 of 2

Chapter 4.5, Problem 21E is Solved
Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

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Two resistors, with resistances R1 and R2, are connected

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