Chapter 12

In Exercises 1-8, make a scatter plot for the given data. Use the scatter plot to describe whether or not the variables appear to be related. $$ \begin{array}{|l|l|l|l|l|l|l|} \hline x & 1 & 6 & 4 & 3 & 7 & 2 \\ \hline y & 2 & 5 & 3 & 3 & 4 & 1 \\ \hline \end{array} $$

In Exercises 1-8, find the percentage of data items in a normal distribution that lie a. below and b. above the given z-score. \(z=0.6\)

The scores on a test are normally distributed with a mean of 100 and a standard deviation of 20. In Exercises 1-10, find the score that is 1 standard deviation above the mean.

In Exercises 1-6, find the range for each group of data items. \(1,2,3,4,5\)

In Exercises \(1-8\), find the mean for each group of data items. \(7,4,3,2,8,5,1,3\)

The government of a large city needs to determine whether the city's residents will support the construction of a new jail. The government decides to conduct a survey of a sample of the city's residents. Which one of the following procedures would be most appropriate for obtaining a sample of the city's residents? a. Survey a random sample of the employees and inmates at the old jail. b. Survey every fifth person who walks into City Hall on a given day. c. Survey a random sample of persons within each geographic region of the city. d. Survey the first 200 people listed in the city's telephone directory.

In Exercises 1-8, make a scatter plot for the given data. Use the scatter plot to describe whether or not the variables appear to be related. $$ \begin{array}{|c|c|c|c|c|c|} \hline x & 2 & 1 & 6 & 3 & 4 \\ \hline y & 4 & 5 & 10 & 8 & 9 \\ \hline \end{array} $$

In Exercises 1-8, find the percentage of data items in a normal distribution that lie a. below and b. above the given z-score. \(z=0.8\)

The scores on a test are normally distributed with a mean of 100 and a standard deviation of 20. In Exercises 1-10, find the score that is 2 standard deviations above the mean.

In Exercises 1-6, find the range for each group of data items. \(16,17,18,19,20\)

In Exercises \(1-8\), find the mean for each group of data items. \(11,6,4,0,2,1,12,0,0\)

The city council of a large city needs to know whether its residents will support the building of three new schools. The council decides to conduct a survey of a sample of the city's residents. Which procedure would be most appropriate for obtaining a sample of the city's residents? a. Survey a random sample of teachers who live in the city. b. Survey 100 individuals who are randomly selected from a list of all people living in the state in which the city in question is located. c. Survey a random sample of persons within each neighborhood of the city. d. Survey every tenth person who enters City Hall on a randomly selected day.

In Exercises 1-8, make a scatter plot for the given data. Use the scatter plot to describe whether or not the variables appear to be related. $$ \begin{array}{|c|c|c|c|c|c|c|c|} \hline x & 8 & 6 & 1 & 5 & 4 & 10 & 3 \\ \hline y & 2 & 4 & 10 & 5 & 6 & 2 & 9 \\ \hline \end{array} $$

In Exercises 1-8, find the percentage of data items in a normal distribution that lie a. below and b. above the given z-score. \(z=1.2\)

The scores on a test are normally distributed with a mean of 100 and a standard deviation of 20. In Exercises 1-10, find the score that is 3 standard deviations above the mean.

In Exercises 1-6, find the range for each group of data items. \(7,9,9,15\)

In Exercises \(1-8\), find the mean for each group of data items. \(91,95,99,97,93,95\)

A questionnaire was given to students in an introductory statistics class during the first week of the course. One question asked, "How stressed have you been in the last \(2 \frac{1}{2}\) weeks, on a scale of 0 to 10 , with 0 being not at all stressed and 10 being as stressed as possible?" The students' responses are shown in the frequency distribution. Use this frequency distribution to solve Exercises 3-6. $$ \begin{aligned} &\begin{array}{|c|c|} \hline \text { Stress Rating } & \text { Frequency } \\ \hline 0 & 2 \\ \hline 1 & 1 \\ \hline 2 & 3 \\ \hline 3 & 12 \\ \hline 4 & 16 \\ \hline 5 & 18 \\ \hline \end{array}\\\ &\begin{array}{|c|c|} \hline \text { Stress Rating } & \text { Frequency } \\ \hline 6 & 13 \\ \hline 7 & 31 \\ \hline 8 & 26 \\ \hline 9 & 15 \\ \hline 10 & 14 \\ \hline \text { Source Joumal of Personality and } \\ \hline \end{array}\\\ &\text { Social Psychology, 69, 1102-1112 } \end{aligned} $$ Which stress rating describes the greatest number of students? How many students responded with this rating?

In Exercises 1-8, make a scatter plot for the given data. Use the scatter plot to describe whether or not the variables appear to be related. $$ \begin{array}{|l|l|l|l|l|} \hline x & 4 & 5 & 2 & 1 \\ \hline y & 1 & 3 & 5 & 4 \\ \hline \end{array} $$

In Exercises 1-8, find the percentage of data items in a normal distribution that lie a. below and b. above the given z-score. \(z=1.4\)

The scores on a test are normally distributed with a mean of 100 and a standard deviation of 20. In Exercises 1-10, find the score that is \(1 \frac{1}{2}\) standard deviations above the mean.

In Exercises 1-6, find the range for each group of data items. \(11,13,14,15,17\)

In Exercises \(1-8\), find the mean for each group of data items. \(100,100,90,30,70,100\)

A questionnaire was given to students in an introductory statistics class during the first week of the course. One question asked, "How stressed have you been in the last \(2 \frac{1}{2}\) weeks, on a scale of 0 to 10 , with 0 being not at all stressed and 10 being as stressed as possible?" The students' responses are shown in the frequency distribution. Use this frequency distribution to solve Exercises 3-6. $$ \begin{aligned} &\begin{array}{|c|c|} \hline \text { Stress Rating } & \text { Frequency } \\ \hline 0 & 2 \\ \hline 1 & 1 \\ \hline 2 & 3 \\ \hline 3 & 12 \\ \hline 4 & 16 \\ \hline 5 & 18 \\ \hline \end{array}\\\ &\begin{array}{|c|c|} \hline \text { Stress Rating } & \text { Frequency } \\ \hline 6 & 13 \\ \hline 7 & 31 \\ \hline 8 & 26 \\ \hline 9 & 15 \\ \hline 10 & 14 \\ \hline \text { Source Joumal of Personality and } \\ \hline \end{array}\\\ &\text { Social Psychology, 69, 1102-1112 } \end{aligned} $$ Which stress rating describes the least number of students? How many responded with this rating?

In Exercises 1-8, find the percentage of data items in a normal distribution that lie a. below and b. above the given z-score. \(z=-0.7\)

The scores on a test are normally distributed with a mean of 100 and a standard deviation of 20. In Exercises 1-10, find the score that is \(2 \frac{1}{2}\) standard deviations above the mean.

In Exercises 1-6, find the range for each group of data items. \(3,3,4,4,5,5\)

In Exercises \(1-8\), find the mean for each group of data items. \(100,40,70,40,60\)

A questionnaire was given to students in an introductory statistics class during the first week of the course. One question asked, "How stressed have you been in the last \(2 \frac{1}{2}\) weeks, on a scale of 0 to 10 , with 0 being not at all stressed and 10 being as stressed as possible?" The students' responses are shown in the frequency distribution. Use this frequency distribution to solve Exercises 3-6. $$ \begin{aligned} &\begin{array}{|c|c|} \hline \text { Stress Rating } & \text { Frequency } \\ \hline 0 & 2 \\ \hline 1 & 1 \\ \hline 2 & 3 \\ \hline 3 & 12 \\ \hline 4 & 16 \\ \hline 5 & 18 \\ \hline \end{array}\\\ &\begin{array}{|c|c|} \hline \text { Stress Rating } & \text { Frequency } \\ \hline 6 & 13 \\ \hline 7 & 31 \\ \hline 8 & 26 \\ \hline 9 & 15 \\ \hline 10 & 14 \\ \hline \text { Source Joumal of Personality and } \\ \hline \end{array}\\\ &\text { Social Psychology, 69, 1102-1112 } \end{aligned} $$ How many students were involved in this study?

In Exercises 1-8, find the percentage of data items in a normal distribution that lie a. below and b. above the given z-score. \(z=-0.4\)

In Exercises 1-6, find the range for each group of data items. \(3,3,3,4,5,5,5\)

A questionnaire was given to students in an introductory statistics class during the first week of the course. One question asked, "How stressed have you been in the last \(2 \frac{1}{2}\) weeks, on a scale of 0 to 10 , with 0 being not at all stressed and 10 being as stressed as possible?" The students' responses are shown in the frequency distribution. Use this frequency distribution to solve Exercises 3-6. $$ \begin{aligned} &\begin{array}{|c|c|} \hline \text { Stress Rating } & \text { Frequency } \\ \hline 0 & 2 \\ \hline 1 & 1 \\ \hline 2 & 3 \\ \hline 3 & 12 \\ \hline 4 & 16 \\ \hline 5 & 18 \\ \hline \end{array}\\\ &\begin{array}{|c|c|} \hline \text { Stress Rating } & \text { Frequency } \\ \hline 6 & 13 \\ \hline 7 & 31 \\ \hline 8 & 26 \\ \hline 9 & 15 \\ \hline 10 & 14 \\ \hline \text { Source Joumal of Personality and } \\ \hline \end{array}\\\ &\text { Social Psychology, 69, 1102-1112 } \end{aligned} $$ How many students had a stress rating of 8 or more?

In Exercises 1-8, find the percentage of data items in a normal distribution that lie a. below and b. above the given z-score. \(z=-1.2\)

In Exercises 7-10, a group of data items and their mean are given. a. Find the deviation from the mean for each of the data item. b. Find the sum of the deviations in part \((a)\). \(3,5,7,12,18,27 ;\) Mean \(=12\)

A random sample of 30 college students is selected. Each student is asked how much time he or she spent on homework during the previous week. The following times (in hours) are obtained: \(16,24,18,21,18,16,18,17,15,21,19,17,17,16,19,18,15,15\), \(20,17,15,17,24,19,16,20,16,19,18,17\). Construct a frequency distribution for the data.

In Exercises 1-8, find the percentage of data items in a normal distribution that lie a. below and b. above the given z-score. \(z=-1.8\)

In Exercises 7-10, a group of data items and their mean are given. a. Find the deviation from the mean for each of the data item. b. Find the sum of the deviations in part \((a)\). \(84,88,90,95,98 ;\) Mean \(=91\)

A random sample of 30 male college students is selected. Each student is asked his height (to the nearest inch). The heights are as follows: $$ \begin{aligned} &72,70,68,72,71,71,71,69,73,71,73,75,66,67,75,74,73,71 \text {, } \\ &72,67,72,68,67,71,73,71,72,70,73,70 . \end{aligned} $$ Construct a frequency distribution for the data.

In Exercises 9-16, find the percentage of data items in a normal distribution that lie between \(z=0.2\) and \(z=1.4\).

In Exercises 7-10, a group of data items and their mean are given. a. Find the deviation from the mean for each of the data item. b. Find the sum of the deviations in part \((a)\). \(29,38,48,49,53,77 ;\) Mean \(=49\)

In Exercises 9–12, find the mean for the data items in the given frequency distribution. $$ \begin{array}{|c|c|} \hline \begin{array}{c} \text { Score } \\ \boldsymbol{x} \end{array} & \begin{array}{c} \text { Frequency } \\ \boldsymbol{f} \end{array} \\ \hline 1 & 1 \\ \hline 2 & 3 \\ \hline 3 & 4 \\ \hline 4 & 4 \\ \hline 5 & 6 \\ \hline 6 & 5 \\ \hline 7 & 3 \\ \hline 8 & 2 \\ \hline \end{array} $$

A college professor had students keep a diary of their social interactions for a week. Excluding family and work situations, the number of social interactions of ten minutes or longer over the week is shown in the following grouped frequency distribution. Use this information to solve Exercises 9-16. $$ \begin{array}{|c|c|} \hline \begin{array}{c} \text { Number of } \\ \text { Social Interactions } \end{array} & \text { Frequency } \\ \hline 0-4 & 12 \\ \hline 5-9 & 16 \\ \hline 10-14 & 16 \\ \hline 15-19 & 16 \\ \hline 20-24 & 10 \\ \hline 25-29 & 11 \\ \hline 30-34 & 4 \\ \hline 35-39 & 3 \\ \hline 40-44 & 3 \\ \hline 45-49 & 3 \\ \hline \end{array} $$ Identify the lower class limit for each class.

In Exercises 9-16, find the percentage of data items in a normal distribution that lie between \(z=0.3\) and \(z=2.1\).

In Exercises 7-10, a group of data items and their mean are given. a. Find the deviation from the mean for each of the data item. b. Find the sum of the deviations in part \((a)\). \(60,60,62,65,65,65,66,67,70,70 ;\) Mean \(=65\)

In Exercises 9–12, find the mean for the data items in the given frequency distribution. $$ \begin{array}{|c|c|} \hline \begin{array}{c} \text { Score } \\ \boldsymbol{x} \end{array} & \begin{array}{c} \text { Frequency } \\ \boldsymbol{f} \end{array} \\ \hline 1 & 2 \\ \hline 2 & 4 \\ \hline 3 & 5 \\ \hline 4 & 7 \\ \hline 5 & 6 \\ \hline 6 & 4 \\ \hline 7 & 3 \\ \hline \end{array} $$

A college professor had students keep a diary of their social interactions for a week. Excluding family and work situations, the number of social interactions of ten minutes or longer over the week is shown in the following grouped frequency distribution. Use this information to solve Exercises 9-16. $$ \begin{array}{|c|c|} \hline \begin{array}{c} \text { Number of } \\ \text { Social Interactions } \end{array} & \text { Frequency } \\ \hline 0-4 & 12 \\ \hline 5-9 & 16 \\ \hline 10-14 & 16 \\ \hline 15-19 & 16 \\ \hline 20-24 & 10 \\ \hline 25-29 & 11 \\ \hline 30-34 & 4 \\ \hline 35-39 & 3 \\ \hline 40-44 & 3 \\ \hline 45-49 & 3 \\ \hline \end{array} $$ Identify the upper class limit for each class.

In Exercises 9-16, find the percentage of data items in a normal distribution that lie between \(z=1\) and \(z=3\).

In Exercises 11-16, find a. the mean; b. the deviation from the mean for each data item; and c. the sum of the deviations in part (b). \(85,95,90,85,100\)

In Exercises 9–12, find the mean for the data items in the given frequency distribution. $$ \begin{array}{|c|c|} \hline \begin{array}{c} \text { Score } \\ \boldsymbol{x} \end{array} & \begin{array}{c} \text { Frequency } \\ \boldsymbol{f} \end{array} \\ \hline 1 & 1 \\ \hline 2 & 1 \\ \hline 3 & 2 \\ \hline 4 & 5 \\ \hline 5 & 7 \\ \hline 6 & 9 \\ \hline 7 & 8 \\ \hline 8 & 6 \\ \hline 9 & 4 \\ \hline 10 & 3 \\ \hline \end{array} $$

A college professor had students keep a diary of their social interactions for a week. Excluding family and work situations, the number of social interactions of ten minutes or longer over the week is shown in the following grouped frequency distribution. Use this information to solve Exercises 9-16. $$ \begin{array}{|c|c|} \hline \begin{array}{c} \text { Number of } \\ \text { Social Interactions } \end{array} & \text { Frequency } \\ \hline 0-4 & 12 \\ \hline 5-9 & 16 \\ \hline 10-14 & 16 \\ \hline 15-19 & 16 \\ \hline 20-24 & 10 \\ \hline 25-29 & 11 \\ \hline 30-34 & 4 \\ \hline 35-39 & 3 \\ \hline 40-44 & 3 \\ \hline 45-49 & 3 \\ \hline \end{array} $$ What is the class width?