Question

at least 99.41% of the data in any data set lie within how many standard deviations of the mean? explain how you arrived at your answer
explain how the number of standard deviations could be found for any data set. choose the correct answer below.
a. use the coefficient of variation.
b. use the empirical rule.
c. use chebychevs theorem.
find the number of standard deviations.
k = □ (round to the nearest integer as needed.)

Explanation:

Step1: Recall Chebychev's Theorem formula

Chebychev's Theorem states that for any number \(k> 0\), at least \(1-\frac{1}{k^{2}}\) of the data lies within \(k\) standard deviations of the mean.

Step2: Set up the equation

We are given that \(1-\frac{1}{k^{2}}=0.9941\).

Step3: Solve for \(k\)

First, rewrite the equation as \(\frac{1}{k^{2}}=1 - 0.9941=0.0059\). Then, \(k^{2}=\frac{1}{0.0059}\approx169.49\). Taking the square - root of both sides, \(k=\sqrt{169.49}\approx13\).

Answer:

\(k = 13\)