Question

question 5
given a set of data that is skewed - left, there is at least ____ % of the data within 3 standard deviations. fill in the blank with the best answer:
0
68
75
88.9
95
99.7

Explanation:

Step1: Recall Chebyshev's theorem

Chebyshev's theorem applies to any distribution (regardless of shape like skewed - left). It 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 \(k = 3\)

When \(k = 3\), we calculate \(1-\frac{1}{k^{2}}=1-\frac{1}{3^{2}}=1 - \frac{1}{9}=\frac{8}{9}\approx0.889\) or \(88.9\%\).

Answer:

88.9