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Get Full Access to Applied Statistics And Probability For Engineers - 6 Edition - Chapter 4.12 - Problem 209se
Get Full Access to Applied Statistics And Probability For Engineers - 6 Edition - Chapter 4.12 - Problem 209se

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# Without an automated irrigation system, the height of ISBN: 9781118539712 55

## Solution for problem 209SE Chapter 4.12

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

Step 3 of 3

##### 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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