The Chebyshev's theorem states that for any data set, regardless of the shape of the distribution, at least (1 - 1/k^2) of the data lie within k standard deviations of the mean, where k is any positive integer greater than 1.

In this case, we are asked to find the number of observations that lie between 23 and 47.

First, we need to calculate the number of standard deviations away from the mean these values are.

The mean is 35 and the standard deviation is 4.

So, 23 is (35 - 23) / 4 = 3 standard deviations below the mean and 47 is (47 - 35) / 4 = 3 standard deviations above the mean.

So, we are looking for the data within 3 standard deviations of the mean.

According to Chebyshev's theorem, at least (1 - 1/3^2) = 1 - 1/9 = 8/9 = 0.8889 or 88.89% of the data lie within 3 standard deviations of the mean.

So, at least 88.89% of 150 observations, which is approximately 133 observations, lie between 23 and 47.

So, the answer is 89%.

Question

The Chebyshev's theorem states that for any data set, regardless of the shape of the distribution, at least (1 - 1/k^2) of the data lie within k standard deviations of the mean, where k is any positive integer greater than 1.

In this case, we are asked to find the number of observations that lie between 23 and 47.

First, we need to calculate the number of standard deviations away from the mean these values are.

The mean is 35 and the standard deviation is 4.

So, 23 is (35 - 23) / 4 = 3 standard deviations below the mean and 47 is (47 - 35) / 4 = 3 standard deviations above the mean.

So, we are looking for the data within 3 standard deviations of the mean.

According to Chebyshev's theorem, at least (1 - 1/3^2) = 1 - 1/9 = 8/9 = 0.8889 or 88.89% of the data lie within 3 standard deviations of the mean.

So, at least 88.89% of 150 observations, which is approximately 133 observations, lie between 23 and 47.

So, the answer is 89%.

Knowee AI · Accepted Answer

The Chebyshev's theorem states that for any data set, regardless of the shape of the distribution, at least (1 - 1/k^2) of the data lie within k standard deviations of the mean, where k is any positive integer greater than 1.

In this case, we are asked to find the number of observations that lie between 23 and 47.

First, we need to calculate the number of standard deviations away from the mean these values are.

The mean is 35 and the standard deviation is 4.

So, 23 is (35 - 23) / 4 = 3 standard deviations below the mean and 47 is (47 - 35) / 4 = 3 standard deviations above the mean.

So, we are looking for the data within 3 standard deviations of the mean.

According to Chebyshev's theorem, at least (1 - 1/3^2) = 1 - 1/9 = 8/9 = 0.8889 or 88.89% of the data lie within 3 standard deviations of the mean.

So, at least 88.89% of 150 observations, which is approximately 133 observations, lie between 23 and 47.

So, the answer is 89%.

As per Chebyshev rule the quantitative data set of size 150 has a mean of 35 and a standard deviation of 4. At least how many observations li between 23 and 47?Group of answer choices89%68%95%75%

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