Dallas Mavericks. From the ESPN website, in the Dallas Mavericks Roster, we obtained the following weights, in pounds, for the players on that basketball team for the 2013–2014 season.

185 270 211 220 235 250 215 200 185 192 240 188 215 176 195 228 189 191 255 245 210 Use the technology of your choice to determine

a. the population mean weight.

b. the population standard deviation of the weights. Note: Depending on the technology that you’re using, you may need to refer to the formula derived in Exercise 3.220(a).

Estimating Relative Standing. In Key Fact 3.3, we stated Chebyshev’s rule: For any quantitative data set and any real number k greater than or equal to 1, at least 1 − 1/k2 of the observations lie within k standard deviations to either side of the mean, that is, between x¯ − k · s and x¯ + k · s. You can use z-scores and Chebyshev’s rule to estimate the relative standing of an observation.

To see how, let us consider again the lengths of the holes at Augusta National Golf Club, shown in the third column of Table 3.17 on page 162. Earlier, we found that the population mean and standard deviation of these lengths are 413.1 yd and 132.0 yd, respectively.

We note, for instance, that the z-score for Pink dogwood’s length of 575 yd is (575 − 413.1)/132.0, or 1.23. Applying Chebyshev’s rule to that z-score, we conclude that at least 1 − 1/1.232, or 33.9%, of the lengths lie within 1.23 standard deviations to either side of the mean. Therefore, Pink dogwood’s length, which is 1.23 standard deviations above the mean, is greater than at least 33.9% of the other holes’ lengths.