Let's solve the question step-by-step to find the probability that a student earns a grade of D.
1. Identify the given data:
- Number of students who earned Grade A = 28
- Number of students who earned Grade B = 35
- Number of students who earned Grade C = 56
- Number of students who earned Grade D = 14
- Number of students who earned Grade F = 7
2. Calculate the total number of students.
To find the total number of students, we add the frequencies of each grade:
[tex]\[
\text{Total number of students} = 28 + 35 + 56 + 14 + 7
\][/tex]
Calculation:
[tex]\[
28 + 35 = 63
\][/tex]
[tex]\[
63 + 56 = 119
\][/tex]
[tex]\[
119 + 14 = 133
\][/tex]
[tex]\[
133 + 7 = 140
\][/tex]
Therefore, the total number of students is 140.
3. Calculate the probability that a student earns a grade of D.
The probability of an event is given by the ratio of the number of favorable outcomes to the total number of outcomes.
In this case, the number of favorable outcomes is the number of students who earned a grade of D, which is 14.
The total number of outcomes is the total number of students, which we calculated to be 140.
So, the probability [tex]\(P(D)\)[/tex] that a student earns a grade of D can be calculated as:
[tex]\[
P(D) = \frac{\text{Number of students who earned Grade D}}{\text{Total number of students}}
\][/tex]
Substituting the values we have:
[tex]\[
P(D) = \frac{14}{140}
\][/tex]
4. Simplify the fraction:
[tex]\[
\frac{14}{140} = \frac{1}{10} = 0.1
\][/tex]
Therefore, the probability that a student earns a grade of D is [tex]\(0.1\)[/tex].
[tex]\[
P(D) = 0.1
\][/tex]
