Assessment 2 Directions: Read, analyze and solve the problem correctly. Show your complete solution with illustration. An agriculturist wants to find out the probability of growing trees more than 50 years. Given that mu = 30 and sigma = 20
Assuming that the age of trees follows a normal distribution with a mean (mu) of 30 and a standard deviation (sigma) of 20, the agriculturist wants to find out the probability of growing trees more than 50 years.
To solve this problem, we need to calculate the z-score of 50 years using the formula:
z = (x - mu) / sigma
where x is the given value (50 years), mu is the mean (30 years), and sigma is the standard deviation (20 years).
z = (50 - 30) / 20
z = 1
This means that the value of 50 years is 1 standard deviation above the mean.
Next, we need to find the area under the standard normal distribution curve to the right of this z-score using a standard normal table or a calculator. The area represents the probability of getting a value more than 50 years.
Using a standard normal table, we find that the area to the right of z = 1 is 0.1587. Therefore, the probability of growing trees more than 50 years is 0.1587 or 15.87%.
Illustration:
The standard normal distribution curve is shown below:
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The mean (mu) is 30 and the standard deviation (sigma) is 20. The value of 50 years is represented by a vertical line on the curve, which is 1 standard deviation above the mean.
We can find the area to the right of this line, which represents the probability of growing trees more than 50 years.
Using a standard normal table or a calculator, we find that the area to the right of z = 1 is 0.1587. Therefore, the probability of growing trees more than 50 years is 0.1587 or 15.87%.
Answers & Comments
Answer:
aral mabuti lods
Step-by-step explanation:
Assuming that the age of trees follows a normal distribution with a mean (mu) of 30 and a standard deviation (sigma) of 20, the agriculturist wants to find out the probability of growing trees more than 50 years.
To solve this problem, we need to calculate the z-score of 50 years using the formula:
z = (x - mu) / sigma
where x is the given value (50 years), mu is the mean (30 years), and sigma is the standard deviation (20 years).
z = (50 - 30) / 20
z = 1
This means that the value of 50 years is 1 standard deviation above the mean.
Next, we need to find the area under the standard normal distribution curve to the right of this z-score using a standard normal table or a calculator. The area represents the probability of getting a value more than 50 years.
Using a standard normal table, we find that the area to the right of z = 1 is 0.1587. Therefore, the probability of growing trees more than 50 years is 0.1587 or 15.87%.
Illustration:
The standard normal distribution curve is shown below:
|
|
|
|
|
-----------|--------------
|
|
|
|
|
The mean (mu) is 30 and the standard deviation (sigma) is 20. The value of 50 years is represented by a vertical line on the curve, which is 1 standard deviation above the mean.
We can find the area to the right of this line, which represents the probability of growing trees more than 50 years.
Using a standard normal table or a calculator, we find that the area to the right of z = 1 is 0.1587. Therefore, the probability of growing trees more than 50 years is 0.1587 or 15.87%.