Let's answer each part of the question step-by-step using the given data in the table.
### Part a: How many people took the exam?
To find the total number of people who took the exam, we need to sum the number of people (frequency, [tex]\( f \)[/tex]) across all the given score ranges:
[tex]\[
8 + 9 + 5 + 5 + 5 = 32
\][/tex]
So, the total number of people who took the exam is [tex]\( \boxed{32} \)[/tex].
### Part b: How many people scored between 67 and 72?
We look at the given table and find the frequency [tex]\( f \)[/tex] for the range 67 to 72, which is 5.
So, the number of people who scored between 67 and 72 is [tex]\( \boxed{5} \)[/tex].
### Part c: What percent of people scored between 67 and 72?
To find the percentage of people who scored between 67 and 72, we use the number of people who scored in that range (5) and the total number of people who took the exam (32). The formula for the percentage is:
[tex]\[
\text{Percentage} = \left( \frac{\text{Number of people who scored between 67 and 72}}{\text{Total number of people}} \right) \times 100
\][/tex]
[tex]\[
\text{Percentage} = \left( \frac{5}{32} \right) \times 100 \approx 15.625
\][/tex]
So, the percent of people who scored between 67 and 72 is [tex]\( \boxed{15.625} \)[/tex].
### Part d: How many people scored 72 or lower?
We need to sum the number of people (frequencies [tex]\( f \)[/tex]) for the ranges that end at 72 or below. These ranges are 55-60, 61-66, and 67-72. Summing these frequencies:
[tex]\[
8 + 9 + 5 = 22
\][/tex]
So, the number of people who scored 72 or lower is [tex]\( \boxed{22} \)[/tex].
### Part e: What percent of people scored above 72?
First, we find the number of people who scored above 72 by subtracting the number of people who scored 72 or lower (22) from the total number of people (32):
[tex]\[
32 - 22 = 10
\][/tex]
Then, we calculate the percentage of people who scored above 72 using the formula:
[tex]\[
\text{Percentage} = \left( \frac{\text{Number of people who scored above 72}}{\text{Total number of people}} \right) \times 100
\][/tex]
[tex]\[
\text{Percentage} = \left( \frac{10}{32} \right) \times 100 \approx 31.25
\][/tex]
So, the percent of people who scored above 72 is [tex]\( \boxed{31.25} \)[/tex].
