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 89% of women have platelet counts within 3 standard deviations of the mean. (round to the nearest integer as needed.) what are the minimum and maximum possible platelet counts that are within 3 standard deviations of the mean? the minimum possible platelet count within 3 standard deviations of the mean is. the maximum possible platelet count within 3 standard deviations of the mean is. (type integers or decimals rounded to one decimal place as needed.)

Explanation:

Step1: Recall the formula for minimum value

The formula for the minimum value within \(k\) standard - deviations of the mean is \(\mu - k\sigma\), where \(\mu\) is the mean and \(\sigma\) is the standard deviation. Here, \(\mu = 255.2\), \(k = 3\), and \(\sigma=65.4\).
\[255.2-3\times65.4\]

Step2: Calculate the minimum value

\[255.2 - 3\times65.4=255.2-196.2 = 59.0\]

Step3: Recall the formula for maximum value

The formula for the maximum value within \(k\) standard - deviations of the mean is \(\mu + k\sigma\).
\[255.2 + 3\times65.4\]

Step4: Calculate the maximum value

\[255.2+3\times65.4=255.2 + 196.2=451.4\]

Answer:

The minimum possible platelet count within 3 standard deviations of the mean is \(59.0\). The maximum possible platelet count within 3 standard deviations of the mean is \(451.4\).