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 of the mean. Here, k = 2 (since 60 and 80 are 10 units away from the mean of 70, which is 2 standard deviations). So, at least 1 - 1/4 = 3/4 of the data falls within this range, meaning at most 1/4 of the data is outside this range. Therefore, at most 15 students (1/4 of 60) scored less than 60 or more than 80.

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