Question
Find the proportion of seniors whose GPA is between 2.8 and 3.15.
the area from 2.1 to 2.8 is .68 and the area from 2.8 to 3.15 is .26
the area from 2.1 to 2.8 is .68 and the area from 2.8 to 3.15 is .26
Answers
Answer
What is the probability that a randomly chosen senior will have a GPA greater than 3.15?
Answered by
GPT-4o mini
To find the proportion of seniors whose GPA is between 2.8 and 3.15, we can use the areas provided.
The area from 2.1 to 2.8 is given as 0.68, and the area from 2.8 to 3.15 is 0.26.
The area under the entire distribution (from 2.1 to the upper limit of the distribution) can be calculated as follows:
1. Calculate the total area from 2.1 to the upper limit (which we can assume includes 3.15 for this context). The total area is the sum of the area from 2.1 to 2.8 and the area from 2.8 to 3.15:
\[
\text{Total area} = \text{Area from } 2.1 \text{ to } 2.8 + \text{Area from } 2.8 \text{ to } 3.15
\]
\[
\text{Total area} = 0.68 + 0.26 = 0.94
\]
2. Since you're interested in the proportion of seniors whose GPA is between 2.8 and 3.15, that area is given as 0.26.
Therefore, the proportion of seniors whose GPA is between 2.8 and 3.15 is **0.26**, or **26%**.
The area from 2.1 to 2.8 is given as 0.68, and the area from 2.8 to 3.15 is 0.26.
The area under the entire distribution (from 2.1 to the upper limit of the distribution) can be calculated as follows:
1. Calculate the total area from 2.1 to the upper limit (which we can assume includes 3.15 for this context). The total area is the sum of the area from 2.1 to 2.8 and the area from 2.8 to 3.15:
\[
\text{Total area} = \text{Area from } 2.1 \text{ to } 2.8 + \text{Area from } 2.8 \text{ to } 3.15
\]
\[
\text{Total area} = 0.68 + 0.26 = 0.94
\]
2. Since you're interested in the proportion of seniors whose GPA is between 2.8 and 3.15, that area is given as 0.26.
Therefore, the proportion of seniors whose GPA is between 2.8 and 3.15 is **0.26**, or **26%**.
Answered by
GPT-4o mini
To determine the probability that a randomly chosen senior will have a GPA greater than 3.15, we need to consider the total area under the GPA distribution.
Given that:
- The area from 2.1 to 2.8 is 0.68.
- The area from 2.8 to 3.15 is 0.26.
From the provided information, we can calculate the total area from 2.1 to a maximum GPA. Assuming that 3.15 is the upper limit of the relevant GPA range, we have already calculated the area from 2.1 to 3.15:
\[
\text{Total area from } 2.1 \text{ to } 3.15 = 0.68 + 0.26 = 0.94
\]
This means that the area under the distribution from 2.1 to the upper limit of the distribution is 0.94.
If we denote the area under the entire distribution, which is typically considered to be 1, we can find the area (and thus the probability) above 3.15 as follows:
\[
\text{Probability(GPA > 3.15)} = 1 - \text{Area from } 2.1 \text{ to } 3.15
\]
\[
\text{Probability(GPA > 3.15)} = 1 - 0.94 = 0.06
\]
Thus, the probability that a randomly chosen senior will have a GPA greater than 3.15 is **0.06**, or **6%**.
Given that:
- The area from 2.1 to 2.8 is 0.68.
- The area from 2.8 to 3.15 is 0.26.
From the provided information, we can calculate the total area from 2.1 to a maximum GPA. Assuming that 3.15 is the upper limit of the relevant GPA range, we have already calculated the area from 2.1 to 3.15:
\[
\text{Total area from } 2.1 \text{ to } 3.15 = 0.68 + 0.26 = 0.94
\]
This means that the area under the distribution from 2.1 to the upper limit of the distribution is 0.94.
If we denote the area under the entire distribution, which is typically considered to be 1, we can find the area (and thus the probability) above 3.15 as follows:
\[
\text{Probability(GPA > 3.15)} = 1 - \text{Area from } 2.1 \text{ to } 3.15
\]
\[
\text{Probability(GPA > 3.15)} = 1 - 0.94 = 0.06
\]
Thus, the probability that a randomly chosen senior will have a GPA greater than 3.15 is **0.06**, or **6%**.
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