91Ó°ÊÓ

The following data set belongs to a population: $$ \begin{array}{ccccccc} 5 & -7 & 2 & 0 & -9 & 1 & 61 \end{array} $$ Calculate the range, variance, and standard deviation.

The following data set belongs to a sample: \(\begin{array}{llllll}14 & 18 & -1 & 08 & 8 & -16\end{array}\) Calculate the range, variance, and standard deviation.

The following data give the number of hot dogs consumed by 10 participants in a hot-dog-eating contest. \(\begin{array}{lllllllll}21 & 17 & 32 & 8 & 20 & 15 & 17 & 23 & 9 & 18\end{array}\) Calculate the range, variance, and standard deviation for these data.

Following are the temperatures (in degrees Fahrenheit) observed during eight wintry days in a midwestern city: \(\begin{array}{llllllll}23 & 14 & 6 & -7 & -2 & 11 & 16 & 19\end{array}\) Compute the range, variance, and standard deviation.

The following data represent the total points scored in each of the NFL championship games played from 2000 through 2009 in that order. \(\begin{array}{lllllllllll}39 & 41 & 37 & 69 & 61 & 45 & 31 & 46 & 31 & 50\end{array}\)

A sample of 2000 observations has a mean of 74 and a standard deviation of 12 . Using Chebyshev's theorem, find at least what percentage of the observations fall in the intervals \(\bar{x} \pm 2 s, \bar{x} \pm 2.5 s\), and \(\bar{x} \pm 3 s\). Note that here \(\bar{x} \pm 2 s\) represents the interval \(\bar{x}-2 s\) to \(\bar{x}+2 s\), and so on.

A large population has a mean of 310 and a standard deviation of 37 . Using the empirical rule, find what percentage of the observations fall in the intervals \(\mu \pm 1 \sigma, \mu \pm 2 \sigma\), and \(\mu \pm 3 \sigma\).

Suppose the average credit card debt for households currently is \(\$ 9500\) with a standard deviation of \(\$ 2600\). a. Using Chebyshev's theorem, find at least what percentage of current credit card debts for all households are between i. \(\$ 4300\) and \(\$ 14,700\) ii. \(\$ 3000\) and \(\$ 16,000\) :b. Using Chebyshev's theorem, find the interval that contains credit card debts of at least \(89 \%\) of all households.

The mean monthly mortgage paid by all home owners in a town is \(\$ 2365\) with a standard deviation of \(\$ 340\) a. Using Chebyshev's theorem, find at least what percentage of all home owners in this town pay a monthly mortgage of i. \(\$ 1685\) to \(\$ 3045\) ii. \(\$ 1345\) to \(\$ 3385\) \({ }^{*} \mathbf{b}\). Using Chebyshev's theorem, find the interval that contains the monthly mortgage payments of at least \(84 \%\) of all home owners.

The prices of all college textbooks follow a bell-shaped distribution with a mean of \(\$ 105\) and a standard deviation of \(\$ 20\). a. Using the empirical rule, find the percentage of all college textbooks with their prices between i. \(\$ 85\) and \(\$ 125\) ii. \(\$ 65\) and \(\$ 145\) \({ }^{*} \mathrm{~b}\). Using the empirical rule, find the interval that contains the prices of \(99.7 \%\) of college textbooks.