Question: The following frequency histogram presents the final grades of a random sample of 100 college…

The following frequency histogram presents the final grades of a random sample of 100 college students.

(a) How many classes are there? There are 11 classes.

(b) What is the class width? The class width is 3.

(c) Which class has the highest frequency? The class 78-80.99 has the highest frequency.

(d) What percentage of students got a final grade lower than 78? The percentage of students who got a final grade lower than 78 is 14%.

Solution

(d) To find the percentage of students who got a final grade lower than 78, you need to count the number of students in the classes with grades below 78: 1. Count the frequency for classes below 78: - 66-68: 3 students - 69-71: 5 students - 72-74: 5 students - 75-77: 7 students 2. Add the frequencies: \[ 3 + 5 + 5 + 7 = 20 \] 3. Calculate the percentage of students with a grade lower than 78: \[ \left( \frac{20}{100} \right) \times 100 = 20\% \] Therefore, 20% of students got a final grade lower than 78.