choose the answer that best describes the chebyshevs rule and fill in the blank with the appropriate…

choose the answer that best describes the chebyshevs rule and fill in the blank with the appropriate percentage value. a. chebyshevs rule says that exactly % of the data values lie within three standard deviations to either side of the mean. b. chebyshevs rule says that at least % of the data values lie within three standard deviations to either side of the mean. c. chebyshevs rule says that approximately % of the data values lie within three standard deviations to either side of the mean.

choose the answer that best describes the chebyshevs rule and fill in the blank with the appropriate percentage value. a. chebyshevs rule says that exactly % of the data values lie within three standard deviations to either side of the mean. b. chebyshevs rule says that at least % of the data values lie within three standard deviations to either side of the mean. c. chebyshevs rule says that approximately % of the data values lie within three standard deviations to either side of the mean.

Answer

Explanation:

Step1: Recall Chebyshev's rule formula

Chebyshev's rule states that for any number (k>1), the proportion of data within (k) standard - deviations of the mean is at least (1-\frac{1}{k^{2}}).

Step2: Substitute (k = 3) into the formula

When (k = 3), we calculate (1-\frac{1}{k^{2}}=1-\frac{1}{3^{2}}=1 - \frac{1}{9}=\frac{8}{9}\approx0.8889) or (88.89%). So at least (88.9%) (rounded) of the data values lie within three standard deviations to either side of the mean.

Answer:

B. Chebyshev's rule says that at least (88.9%) of the data values lie within three standard deviations to either side of the mean.