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Without an automated irrigation system, the height of

Applied Statistics and Probability for Engineers | 6th Edition | ISBN: 9781118539712 | Authors: Douglas C. Montgomery, George C. Runger ISBN: 9781118539712 55

Solution for problem 209SE Chapter 4.12

Applied Statistics and Probability for Engineers | 6th Edition

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Applied Statistics and Probability for Engineers | 6th Edition | ISBN: 9781118539712 | Authors: Douglas C. Montgomery, George C. Runger

Applied Statistics and Probability for Engineers | 6th Edition

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Problem 209SE

Problem 209SE

Without an automated irrigation system, the height of plants two weeks after germination is normally distributed with a mean of 2.5 centimeters and a standard deviation of 0.5 centimeter.

(a) What is the probability that a plant’s height is greater than 2.25 centimeters?

(b) What is the probability that a plant’s height is between 2.0 and 3.0 centimeters?

(c) What height is exceeded by 90% of the plants?

Step-by-Step Solution:
Step 1 of 3

Solution 209SE

Step1 of 4:

Let us consider a random variable X presents the the height of plants two weeks after germination. And X is normally distributed with mean and standard deviation

Here our goal is:

a). We need to find the probability that a plant’s height is greater than 2.25 centimeters.

b). We need to find the probability that a plant’s height is between 2.0 and 3.0 centimeters.

c). We need to find the height which is exceeded by 90% of the plants.


Step2 of 4:

a).

Consider,

   

                         

                           

                   

Where, is obtained from standard normal table(area under normal curve).

(In area under normal curve we have to see in row -0.5 under column 0.00)

Hence,

                 

             

Therefore,


Step3 of 4:

b).

Consider,

   

                           

                 

               

Where, is obtained from standard normal table(area under normal curve).

(In area under normal curve we have to see in row -1.0 under column 0.00)

(In area under normal curve we have to see in row 1.0 under column 0.00)

Hence,

                 

   

Therefore,


Step4 of 4:

c).

We have (1 - ) = 0.90,

                        = 1 - 0.90

                           = 0.10

Hence,

               

Where, is obtained from standard normal table(area under normal curve). In area under normal curve we have see where 0.10 value falls, it falls in row -1.2 under column 0.08.

The corresponding value is the mean increased by the product of the Z score and the standard deviation:

 

               

 

Therefore, x = 1.86.


Step 2 of 3

Chapter 4.12, Problem 209SE is Solved
Step 3 of 3

Textbook: Applied Statistics and Probability for Engineers
Edition: 6
Author: Douglas C. Montgomery, George C. Runger
ISBN: 9781118539712

Applied Statistics and Probability for Engineers was written by and is associated to the ISBN: 9781118539712. The answer to “Without an automated irrigation system, the height of plants two weeks after germination is normally distributed with a mean of 2.5 centimeters and a standard deviation of 0.5 centimeter.(a) What is the probability that a plant’s height is greater than 2.25 centimeters?(b) What is the probability that a plant’s height is between 2.0 and 3.0 centimeters?(c) What height is exceeded by 90% of the plants?” is broken down into a number of easy to follow steps, and 65 words. The full step-by-step solution to problem: 209SE from chapter: 4.12 was answered by , our top Statistics solution expert on 07/28/17, 07:57AM. This textbook survival guide was created for the textbook: Applied Statistics and Probability for Engineers , edition: 6. Since the solution to 209SE from 4.12 chapter was answered, more than 499 students have viewed the full step-by-step answer. This full solution covers the following key subjects: height, centimeters, Probability, plant, plants. This expansive textbook survival guide covers 97 chapters, and 2005 solutions.

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