In a class of 950, approximately how many students will receive each letter grade according to the grading system where: Numerical grades (X) interval Grade X ≥ µ + 1.6 σ A µ + 0... In a class of 950, approximately how many students will receive each letter grade according to the grading system where: Numerical grades (X) interval Grade X ≥ µ + 1.6 σ A µ + 0.8σ ≤ X < µ + 1.6σ B µ - 0.8σ ≤ X < µ + 0.8σ C µ - 1.6σ ≤ X < µ - 0.8σ D X < µ - 1.6σ F Give your answer to the nearest whole number.
Understand the Problem
The question describes a grading system based on the normal distribution (bell curve) with given intervals based on the mean (µ) and standard deviation (σ) to calculate the approximate number of students that will receive each letter grade in class of n = 950.
Answer
A: 67 B: 228 C: 361 D: 228 F: 67
Answer for screen readers
A: 67
B: 228
C: 361
D: 228
F: 67
Steps to Solve
- Calculate the percentage of students for each grade based on the normal distribution:
The problem gives intervals based on standard deviations for each letter grade in a normally distributed dataset
A: $x > \mu + 1.5\sigma$ which corresponds to approximately 7% of students
B: $\mu + 0.5\sigma < x \le \mu + 1.5\sigma$ which corresponds to approximately 24% of students
C: $\mu - 0.5\sigma < x \le \mu + 0.5\sigma$ which corresponds to approximately 38% of students
D: $\mu - 1.5\sigma < x \le \mu - 0.5\sigma$ which corresponds to approximately 24% of students
F: $x \le \mu - 1.5\sigma$ which corresponds to approximately 7% of students
- Calculate the number of students for each grade:
Multiply the percentage of students for each grade with the total number of students (950)
A: $0.07 \cdot 950 $
B: $0.24 \cdot 950$
C: $0.38 \cdot 950$
D: $0.24 \cdot 950$
F: $0.07 \cdot 950$
- Round results to the nearest whole number:
A: $0.07 \cdot 950 = 66.5 \approx 67$
B: $0.24 \cdot 950 = 228$
C: $0.38 \cdot 950 = 361$
D: $0.24 \cdot 950 = 228$
F: $0.07 \cdot 950 = 66.5 \approx 67$
A: 67
B: 228
C: 361
D: 228
F: 67
More Information
The grading distribution follows a normal distribution, where most students receive a C, and fewer students receive A's or F's.
Tips
A common mistake is not rounding the number of students to the nearest whole number, since you can't have a fraction of a student.
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