Mr. Doodle’s grade distribution over the past 3 years for a course in college algebra is shown in the chart below.
Grade Number
A 45
B 180
C 110
D 95
F 65
I 5
If Jane plans to take a college algebra course with Mr. Doodle, determine the empirical probability that she receives at least a B.
P = 180 / (45+180+110+95+5) = 180/500 =
9/25 = 0.36.
To determine the empirical probability that Jane receives at least a B in the college algebra course with Mr. Doodle, we need to consider the number of students who received a B or higher, and divide it by the total number of students.
In this case, the grades that are B or higher are A, B, and C. We need to sum up the number of students who received these grades.
Number of students who received at least a B = Number of students who received B + Number of students who received A + Number of students who received C = 180 + 45 + 110 = 335
Now, we need to divide this number by the total number of students to find the empirical probability.
Total number of students = Sum of the number of students for each grade = 45 + 180 + 110 + 95 + 65 + 5 = 500
Empirical probability of receiving at least a B = Number of students who received at least a B / Total number of students = 335 / 500 = 0.67
Therefore, the empirical probability that Jane receives at least a B in the college algebra course with Mr. Doodle is 0.67, or 67%.