Questions: The following figure is a probability density curve that represents the grade point averages (GPA) of the graduating seniors at a large university. Find the proportion of seniors whose GPA is between 3.8 and 4 The proportion of seniors whose GPA is between 3.8 and 4 is

The following figure is a probability density curve that represents the grade point averages (GPA) of the graduating seniors at a large university.

Find the proportion of seniors whose GPA is between 3.8 and 4 The proportion of seniors whose GPA is between 3.8 and 4 is

Transcript text: The following figure is a probability density curve that represents the grade point averages (GPA) of the graduating seniors at a large university. Find the proportion of seniors whose GPA is between 3.8 and 4 The proportion of seniors whose GPA is between 3.8 and 4 is $\square$

Solution

Solution Steps

Step 1: Identify the relevant area

The question asks for the proportion of seniors whose GPA is between 3.8 and 4. This corresponds to the area under the curve between _x_ = 3.8 and _x_ = 4.

Step 2: Calculate the area

The area under the curve to the right of _x_ = 3.8 has the value of 0.26. The area under the entire curve should be equal to 1. The problem gives us the area to the left of _x_ = 3.8 is equal to 0.63. The area to the right of _x_ = 4 is not explicitly given. It is found by subtracting the areas from the total area of 1. 1 - 0.63 - 0.26 = 0.11. Therefore, the area between 3.8 and 4. is 0.26 - 0.11 = 0.15. The other way to solve this is add 0.63 and 0.26 together which gives 0.89. Subtract this value from 1 which also yields 0.11. The area between 3.8 and 4. can be calculated by taking the total area to the right of 3.8 (which is 0.26) and subtracting the total area to the right of 4 (0.11) so 0.26 - 0.11 = 0.15.

Final Answer:

0.15

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