Chebyshev's theorem states that at least 1 - 1/k^2 of data from a sample will fall within k standard deviations from the mean for any k 1.

In this case, we want to find the number of students who scored less than 60 or more than 80. This is equivalent to finding the number of students who scored more than 2 standard deviations away from the mean (since the mean is 70 and the standard deviation is 5, 2 standard deviations is 10, so scores less than 60 or more than 80 are more than 2 standard deviations away from the mean).

Using Chebyshev's theorem with k = 2, we find that at least 1 - 1/2^2 = 1 - 1/4 = 0.75 or 75% of the data will fall within 2 standard deviations from the mean. This means that at most 25% of the data will fall more than 2 standard deviations from the mean.

Since there are 60 students in the class, this means that at most 0.25 * 60 = 15 students scored less than 60 or more than 80.

So, the answer is "At most 15".

Question

Chebyshev's theorem states that at least 1 - 1/k^2 of data from a sample will fall within k standard deviations from the mean for any k > 1.

In this case, we want to find the number of students who scored less than 60 or more than 80. This is equivalent to finding the number of students who scored more than 2 standard deviations away from the mean (since the mean is 70 and the standard deviation is 5, 2 standard deviations is 10, so scores less than 60 or more than 80 are more than 2 standard deviations away from the mean).

Using Chebyshev's theorem with k = 2, we find that at least 1 - 1/2^2 = 1 - 1/4 = 0.75 or 75% of the data will fall within 2 standard deviations from the mean. This means that at most 25% of the data will fall more than 2 standard deviations from the mean.

Since there are 60 students in the class, this means that at most 0.25 * 60 = 15 students scored less than 60 or more than 80.

So, the answer is "At most 15".

Knowee AI · Accepted Answer

Chebyshev's theorem states that at least 1 - 1/k^2 of data from a sample will fall within k standard deviations from the mean for any k > 1.

In this case, we want to find the number of students who scored less than 60 or more than 80. This is equivalent to finding the number of students who scored more than 2 standard deviations away from the mean (since the mean is 70 and the standard deviation is 5, 2 standard deviations is 10, so scores less than 60 or more than 80 are more than 2 standard deviations away from the mean).

Using Chebyshev's theorem with k = 2, we find that at least 1 - 1/2^2 = 1 - 1/4 = 0.75 or 75% of the data will fall within 2 standard deviations from the mean. This means that at most 25% of the data will fall more than 2 standard deviations from the mean.

Since there are 60 students in the class, this means that at most 0.25 * 60 = 15 students scored less than 60 or more than 80.

So, the answer is "At most 15".

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.Multiple ChoiceAt least 15At most 15At least 45At most 45

Question

Solution

Similar Questions

Upgrade your grade with Knowee