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.

Question

Mathematics

Sheldon Mcclain

10 May, 08:53

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.

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Answers (1)

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Gretchen Munoz · Answer 1

At most 15 students scored less than 60 or more than 80.

Step-by-step explanation:

Chebyshev's Theorem states that:

At least 75% of the measures are within 2 standard deviations of the mean.

At least 89% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 70

Standard deviation = 5

Use Chebyshev's theorem to determine the number of students who scored less than 60 or more than 80.

60 = 70 - 2*5

So 60 is two standard deviations below the mean

80 = 70 + 2*5

So 80 is two standard deviations above the mean.

By the Chebyshev's theorem, at least 75% of the students scored between 60 and 80. So at most 25% scored less than 60 or more than 80.

0.25*60 = 15

At most 15 students scored less than 60 or more than 80.