91Ó°ÊÓ

Suppose that on a certain section of I-95 with a posted speed limit of \(65 \mathrm{mph}\), the speeds of all vehicles have a bell-shaped distribution with a mean of \(72 \mathrm{mph}\) and a standard deviation of \(3 \mathrm{mph}\). a. Using the empirical rule, find the percentage of vehicles with the following speeds on this section of I-95. i. 63 to \(81 \mathrm{mph}\) ii. 69 to \(75 \mathrm{mph}\) *b. Using the empirical rule, find the interval that contains the speeds of \(95 \%\) of vehicles traveling on this section of \(\mathrm{I}-95\).

Briefly describe how the three quartiles are calculated for a data set. Illustrate by calculating the three quartiles for two examples, the first with an odd number of observations and the second with an even number of observations.

The following data give the speeds of 13 cars (in mph) measured by radar, traveling on I-84. \(\begin{array}{lllllll}73 & 75 & 69 & 68 & 78 & 69 & 74 \\\ 76 & 72 & 79 & 68 & 77 & 71 & \end{array}\) a. Find the values of the three quartiles and the interquartile range. b. Calculate the (approximate) value of the 35 th percentile. c. Compute the percentile rank of 71 .

The following data give the numbers of new cars sold at a dealership during a 20 -day period. \(\begin{array}{lrlrlllll}8 & 5 & 12 & 3 & 9 & 10 & 6 & 12 & 8 \\\ 4 & 16 & 10 & 11 & 7 & 7 & 3 & 5 & 9\end{array}\) a. Calculate the values of the three quartiles and the interquartile range. Where does the value of 4 lie in relation to these quartiles? b. Find the (approximate) value of the 25 th percentile. Give a brief interpretation of this percentile. c. Find the percentile rank of 10 . Give a brief interpretation of this percentile rank.

Prepare a box-and-whisker plot for the following data: \(\begin{array}{llllllll}36 & 43 & 28 & 52 & 41 & 59 & 47 & 61 \\ 24 & 55 & 63 & 73 & 32 & 25 & 35 & 49 \\ 31 & 22 & 61 & 42 & 58 & 65 & 98 & 34\end{array}\)

Refer to Exercise 3.22. The following data give the number of students suspended for bringing weapons to schools in the Tri-City School District for each of the past 12 weeks. 59 \(\begin{array}{lllllllll}21 & 17 & 6 & 9 & 1 & 01 & 43 & 6 & 5\end{array}\) Make a box-and-whisker plot. Comment on the skewness of these data

The following data give the numbers of new cars sold at a dealership during a 20-day period. \(\begin{array}{llrlrlrlrll}8 & 5 & 1 & 2 & 3 & 9 & 1 & 06 & 1 & 28 & 8 & \\ 4 & 1 & 61 & 01 & 17 & 7 & 3 & 5 & 9 & 1 & 1\end{array}\) Make a box-and-whisker plot. Comment on the skewness of these data.

The following data give the numbers of driving citations received by 12 drivers. \(\begin{array}{llllllllllll}4 & 8 & 0 & 3 & 1 & 17 & 4 & 1 & 48 & 1 & 37 & 9\end{array}\) a. Find the mean, median, and mode for these data. b. Calculate the range, variance, and standard deviation. c. Are the values of the summary measures in parts a and b population parameters or sample statistics?

The mean time taken to learn the basics of a word processor by all students is 200 minutes with a standard deviation of 20 minutes. a. Using Chebyshev's theorem, find at least what percentage of students will learn the basics of this word processor in i. 160 to 240 minutes ii. 140 to 260 minutes \({ }^{*}\) b. Using Chebyshev's theorem, find the interval that contains the time taken by at least \(75 \%\) of all students to learn this word processor.

Refer to Exercise \(3.115\). Suppose the times taken to learn the basics of this word processor by all students have a bell-shaped distribution with a mean of 200 minutes and a standard deviation of 20 minutes. a. Using the empirical rule, find the percentage of students who will learn the basics of this word processor in i. 180 to 220 minutes ii. 160 to 240 minutes "b. Using the empirical rule, find the interval that contains the time taken by \(99.7 \%\) of all students to learn this word processor.