Question: Analyzing Weights of Supermodels. Supermodels are sometimes criticized on the grounds that their low weights encourage unhealthy eating habits among young women. Listed below are the weights (in pounds) of nine randomly selected supermodels.

Find each of the following:

1. mean
2. median
3. mode
4. midrange
5. range
6. variance
7. standard deviation
8. \(Q_{1}\)
9. \(Q_{2}\)

j: \(Q_{3}\)

k. What is the level of measurement of these data (nominal, ordinal, interval, ratio)?

l. Construct a boxplot for the data.

m. Construct a \(99 \%\) confidence interval for the population mean.

n. Construct a \(99 \%\) confidence interval for the standard deviation \(\sigma\).

o. Find the sample size necessary to estimate the mean weight of all supermodels so that there is \(99 \%\) confidence that the sample mean is in error by no more than \(2 \mathrm{lb}\). Use the sample standard deviation \(s\) from part (g) as an estimate of the population standard deviation \(\sigma\).

p. When women are randomly selected from the general population, their weights are normally distributed with a mean of \(143 \mathrm{lb}\) and a standard deviation of \(29 \mathrm{lb}\) (based on data from the National Health and Examination Survey). Based on the given sample values, do the weights of supermodels appear to be substantially less than the weights of randomly selected women? Explain.

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