Question

you have data from an unknown distribution. you are told that this data - set has a population mean μ = 8640 with population standard deviation σ = 841. your professor wants to know the percentage of data that can be found within 2.00 standard deviations to either side of the mean. you quickly assert, \i know that at least blank % of the data will be within 2.00 standard deviations to either side of the mean.\ answer as a percent with one decimal place

Explanation:

Step1: Apply Chebyshev's theorem

Chebyshev's theorem states that for any data set (regardless of the shape of its distribution), the proportion of data within \(k\) standard - deviations of the mean is at least \(1-\frac{1}{k^{2}}\), where \(k>1\). Here, \(k = 2\).

Step2: Calculate the proportion

Substitute \(k = 2\) into the formula \(1-\frac{1}{k^{2}}\). We get \(1-\frac{1}{2^{2}}=1 - \frac{1}{4}=\frac{3}{4}=0.75\).

Step3: Convert to percentage

To convert the proportion to a percentage, multiply by 100. So \(0.75\times100 = 75.0\%\).

Answer:

75.0%