Answer :
Let's break down the information and solve the problem step-by-step.
Dak took an exam and scored 63 points, placing him in the 95th percentile. There were 165 students who took the exam.
### Part a: What percent of students scored at or below 63 points?
Since Dak is in the 95th percentile, this means that 95% of the students scored at or below his score of 63 points.
Answer for a: 95%
### Part b: What percent of students scored higher than Dak?
To find the percent of students who scored higher than Dak, we need to subtract the percent of students who scored at or below his score from 100%.
- Percent of students who scored higher than Dak = 100% - 95%
Answer for b: 5%
### Part c: How many students scored the same as Dak or lower? Round to an integer.
To find the number of students who scored the same as Dak or lower (i.e., at or below the 95th percentile), we can use the total number of students and multiply it by the percentile (as a decimal).
- Number of students who scored the same or lower = 95% of 165 students
- Converting the percentile to a decimal: 95% = 0.95
- Calculating the number of students: [tex]\( 0.95 \times 165 = 156.75 \)[/tex]
Since the number of students must be a whole number, we will round 156.75 to the nearest integer.
Answer for c: 157 students
Thus, the detailed answers are:
a. 95% of the students scored at or below 63 points.
b. 5% of the students scored higher than Dak.
c. 157 students scored the same as Dak or lower.
Dak took an exam and scored 63 points, placing him in the 95th percentile. There were 165 students who took the exam.
### Part a: What percent of students scored at or below 63 points?
Since Dak is in the 95th percentile, this means that 95% of the students scored at or below his score of 63 points.
Answer for a: 95%
### Part b: What percent of students scored higher than Dak?
To find the percent of students who scored higher than Dak, we need to subtract the percent of students who scored at or below his score from 100%.
- Percent of students who scored higher than Dak = 100% - 95%
Answer for b: 5%
### Part c: How many students scored the same as Dak or lower? Round to an integer.
To find the number of students who scored the same as Dak or lower (i.e., at or below the 95th percentile), we can use the total number of students and multiply it by the percentile (as a decimal).
- Number of students who scored the same or lower = 95% of 165 students
- Converting the percentile to a decimal: 95% = 0.95
- Calculating the number of students: [tex]\( 0.95 \times 165 = 156.75 \)[/tex]
Since the number of students must be a whole number, we will round 156.75 to the nearest integer.
Answer for c: 157 students
Thus, the detailed answers are:
a. 95% of the students scored at or below 63 points.
b. 5% of the students scored higher than Dak.
c. 157 students scored the same as Dak or lower.
