The grade distribution of the students in a geometry class is as follows.
| Grade | A | B | C | D | F |
| :---- | :- | :- | :- | :- | :- |
| Frequency | 28 | 35 | 56 | 14 | 7 |
Find the probability that a student earns a grade of B.
[tex]P(B)=?[/tex]
Answer (2)
Calculate the total number of students: T = 28 + 35 + 56 + 14 + 7 = 140 .
Calculate the probability of a student earning a grade of B: P ( B ) = 140 35 .
Simplify the fraction: P ( B ) = 140 35 = 4 1 .
The probability that a student earns a grade of B is: 4 1 .
Explanation
Understand the problem We are given the grade distribution of students in a geometry class and asked to find the probability that a student earns a grade of B. To do this, we need to divide the number of students who received a B by the total number of students in the class.
Calculate the total number of students First, we need to find the total number of students in the class. We can do this by summing the frequencies of all the grades: T = 28 + 35 + 56 + 14 + 7 = 140 So, there are 140 students in total.
Calculate the probability of earning a grade of B Next, we need to find the probability of a student earning a grade of B. The frequency of students with a grade of B is 35. So, we divide the frequency of grade B by the total number of students: P ( B ) = 140 35 Now, we simplify the fraction: P ( B ) = 140 35 = 140 ÷ 35 35 ÷ 35 = 4 1 So, the probability that a student earns a grade of B is 4 1 .
State the final answer The probability that a student earns a grade of B is 4 1 , which is equal to 0.25.
Examples
Imagine you're analyzing student performance in a large class to understand how grades are distributed. Calculating the probability of students achieving a particular grade, like a 'B,' helps identify areas where students might need more support. For example, if the probability of getting a 'B' is low, it might indicate that the course material is challenging or that the grading criteria are stringent. This analysis can inform teaching strategies and curriculum adjustments to improve student outcomes. In this case, we calculated the probability as follows: P ( B ) = 140 35 = 4 1 = 0.25 , meaning there's a 25% chance a student gets a 'B'.
The probability that a student earns a grade of B in the geometry class is 4 1 or 25%. This was calculated by dividing the number of students who received a B by the total number of students in the class. There are 140 students in total, and 35 of them earned a B.
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