In a marketing class of 60 students, the mean and the standard deviation of scores was 70 and 5, respectively. Use Chebyshev's theorem to determine the number of students who scored less than 60 or more than 80.
A) At least 45
B) At most 15
C) At most 45
D) At least 15

Question

Quizplus · Accepted Answer

Chebyshev's theorem states that at least (1 - 1/k^2) of data falls within k standard deviations from the mean. For scores less than 60 or more than 80, k = 2 (since 60 and 80 are 2 standard deviations away from the mean of 70). Thus, at least 1 - 1/4 = 0.75 of the students scored between 60 and 80, meaning at most 25% (or 15 students) scored less than 60 or more than 80.

In a Marketing Class of 60 Students, the Mean and the Standard