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Refer to Exercise 5. Suppose 10 circuits are constructed.

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 6E Chapter 4.6

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 6E

Problem 6E

Refer to Exercise 5. Suppose 10 circuits are constructed. Find the probability that 8 or more have voltages less than 200 volts.

Step-by-Step Solution:
Step 1 of 3

Solution 6E

Step1 of 3:

Let us consider resistance R in ohms it follows lognormal distribution with mean and variance

That is

Also current I amperes it follows lognormal distribution with mean and variance

That is

We need to find the probability that 8 or more have voltages less than 200 volts.


Step2 of 3:

Consider,

               

               

           

     

Here is obtained from statistical table(area under normal curve)

(In a standard normal table we have to see in row 0.5 under column 0.04)

 

                = 0.7054

Hence, =0.7054.


Step3 of 3:

If we construct 10 circuits then the probability that 8 or more have voltages less than 200 volts is given by

Here is obtained from Excel by using the function “=Binomdist(x,n,p,false)”.

X

P(X>8)

8

0.2394206698

9

0.1273948408

10

0.03050384274

 

Therefore, the probability that 8 or more have voltages less than 200 volts is 0.0305.


 

Step 2 of 3

Chapter 4.6, Problem 6E is Solved
Step 3 of 3

Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

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Refer to Exercise 5. Suppose 10 circuits are constructed.