Question

using the accompanying table of data, blood platelet counts of women have a bell - shaped distribution with a mean of 255.2 and a standard deviation of 65.4. (all units are 1000 cells/μl.) using chebyshevs theorem, what is known about the percentage of women with platelet counts that are within 3 standard deviations of the mean? what are the minimum and maximum possible platelet counts that are within 3 standard deviations of the mean? click the icon to view the table of platelet counts. using chebyshevs theorem, what is known about the percentage of women with platelet counts that are within 3 standard deviations of the mean? at least % of women have platelet counts within 3 standard deviations of the mean. (round to the nearest integer as needed.)

Explanation:

Step1: Recall Chebyshev's theorem formula

Chebyshev's theorem states that for any number \(k>1\), the proportion of data within \(k\) standard - deviations of the mean is at least \(1-\frac{1}{k^{2}}\). Here \(k = 3\).

Step2: Calculate the percentage

Substitute \(k = 3\) into the formula \(1-\frac{1}{k^{2}}\). We get \(1-\frac{1}{3^{2}}=1 - \frac{1}{9}=\frac{8}{9}\approx0.8889\). To convert this to a percentage, we multiply by 100: \(0.8889\times100 = 88.89\%\). Rounding to the nearest integer, we have \(89\%\).

Answer:

89