A set of data is NOT NORMALLY DISTRIBUTED. The mean is 300, and the standard deviation is 10. According to Chebyshev's Theorem, atleast what percent of the data would lie between 270 and 330? The farthest I got was 1- 1/10squared x 100% = .99, I am not sure if this is correct or not? Can someone help? Thanks
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Yes, you are correct in using Chebyshev's Theorem to solve this problem. Chebyshev's Theorem applies to any distribution, regardless of its shape. It states that for any set of data, regardless of whether it is normally distributed or not, at least (1 - 1/k^2) percent of the data will fall within k standard deviations of the mean.
In this case, the mean is 300 and the standard deviation is 10. So, we can substitute these values into the formula: (1 - 1/k^2) percent of the data will lie within k standard deviations of the mean.
To find out how much of the data lies between 270 and 330, we need to calculate k. Since the interval is centered around the mean (300), we can find k by taking the difference between the mean and one end of the interval, and dividing it by the standard deviation.
k = (330 - 300) / 10 = 3
Now, substitute the value of k into the formula and calculate the percentage of data that falls within 3 standard deviations of the mean:
(1 - 1/3^2) = (1 - 1/9) = 8/9 ≈ 0.8889
So, at least 88.89% (rounded to two decimal places) of the data will lie between 270 and 330.