Chapter 15

What are the first, second, and third quartiles for the set of integers from 1 to 100\(?\)

Suggest a method that might be used to collect data for each study. Tell whether your method uses a population or a sample. Population of each of the states of the United States

In \(15-19\) a. Draw a scatter plot for each data set. Based on the scatter plot, would the correlation coefficient be close to \(-1,0,\) or 1\(?\) Explain. c. Use a calculator to find the correlation coefficient for each set of data. An economist is studying the job market in a large city conducts of survey on the number of jobs in a given neighborhood and the number of jobs paying \(\$ 100,000\) or more a year. A sample of 10 randomly selected neighborhood yields the following data:

A librarian estimates that the average number of books checked out by a library patron is 4 with a standard deviation of 2 books. If the number of books checked out each day approximates a normal distribution, what percent of the library patrons checked out more than 7 books yesterday?

To commute to the high school in which Mr. Fedora teaches, he can take either the Line A or the Line B train. Both train stations are the same distance from his house and both stations report that, on average, they run 10 minutes late from the scheduled arrival time. However, the standard deviation for Line A is 1 minute and the standard deviation for Line B is 5 minutes. To arrive at approximately the same time on a regular basis, which train line should Mr. Fedora use? Explain.

What are the first, second, and third quartiles for the set of integers from 0 to 100\(?\)

Suggest a method that might be used to collect data for each study. Tell whether your method uses a population or a sample. Heights of children entering kindergarten

The heights of a group of women are normally distributed with a mean of 170 centimeters and a standard deviation of 10 centimeters. What is the \(z\) -score of a member of the group who is 165 centimeters tall?

Suggest a method that might be used to collect data for each study. Tell whether your method uses a population or a sample. Popularity of a new movie

The following table shows the speed in megahertz of Intel computer chips over the course of 36 years. The time is given as the number of years since \(1971 .\) $$ \begin{array}{|c|c|c|c|c|c|c|c|}\hline \text { Year } & {0} & {1} & {3} & {7} & {11} & {14} & {18} & {22} \\ \hline \text { Speed } & {0.108} & {0.8} & {2} & {5} & {6} & {16} & {25} & {66} \\ \hline \text { Year } & {24} & {26} & {28} & {29} & {31} & {34} & {35} & {36} \\ \hline \text { Speed } & {200} & {300} & {500} & {1,500} & {1,700} & {3,200} & {2,900} & {3,000} \\\ \hline\end{array} $$ One application of Moore's Law is that the speed of a computer processor should double approximately every two years. Use this information to determine the regression model. Does Moore's Law hold for Intel computer chips? Explain.

In \(15-19\) a. Draw a scatter plot for each data set. Based on the scatter plot, would the correlation coefficient be close to \(-1,0,\) or 1\(?\) Explain. c. Use a calculator to find the correlation coefficient for each set of data. The table below shows the five-day forecast and the actual high temperature for the fifth day over the course of 18 days. The temperature is given in degrees Fahrenheit.

The test grades for a standardized test are normally distributed with a mean of \(50 .\) A grade of 60 represents a z-score of \(1.25 .\) What is the standard deviation of the data?

The ages of all of the students in a science class are shown in the table. Find the variance and the standard deviation. \(\begin{array}{|c|c|}\hline \text { Age } & {\text { Frequency }} \\ \hline 18 & {1} \\ {17} & {2} \\ {16} & {9} \\ {15} & {9} \\ \hline\end{array}\)

The weights in pounds of the members of the football team are shown below: $$\begin{array}{cccccccccc}{181} & {199} & {178} & {203} & {211} & {208} & {209} & {202} & {212} & {194} \\ {185} & {208} & {223} & {206} & {202} & {213} & {202} & {186} & {189} & {203}\end{array}$$ a. Find the mean. b. Find the median. c. Find the mode or modes. d. Find the first and third quartiles. e. Draw a box-and-whisker plot.

The grades on a math test of 25 students are listed below. $$\begin{array}{llllllllllll}{86} & {92} & {77} & {84} & {75} & {95} & {66} & {88} & {84} & {53} & {98} & {87} & {83} \\ {74} & {61} & {82} & {93} & {98} & {87} & {77} & {86} & {58} & {72} & {76} & {89}\end{array}$$ a. Organize the data in a stem-and-leaf diagram. b. Organize the data in a frequency distribution table. c. How many students scored 70 or above on the test? d. How many students scored 60 or below on the test?

Nora scored 88 on a math test that had a mean of 80 and a standard deviation of \(5 .\) She also scored 80 on a science test that had a mean of 70 and a standard deviation of \(3 .\) On which test did Nora perform better compared with other students who took the tests?

The table shows the number of correct answers on a test consisting of 15 questions. The table represents correct answers for a sample of the students who took the test. Find the standard deviation based on this sample. \(\begin{array}{|c|c|c|c|c|c|c|c|c|}\hline \text { Correct } & {6} & {7} & {8} & {9} & {10} & {11} & {12} & {13} & {14} & {15} \\ \hline \text { Frequency } & {2} & {1} & {3} & {3} & {5} & {8} & {8} & {5} & {4} & {1} \\\ \hline\end{array}\)

The ages of students in a calculus class at a high school are shown in the table. Find the mean and median age. $$ \begin{array}{|c|c|}\hline \text { Age } & {\text { Frequency }} \\ \hline 19 & {2} \\ {18} & {8} \\ {17} & {9} \\ {16} & {1} \\ {15} & {1} \\\ \hline\end{array} $$

Mrs. Gillis gave a test to her two classes of algebra. The mean grade for her class of 20 students was 86 and the mean grade of her class of 15 students was \(79 .\) What is the mean grade when she combines the grades of both classes?

The table shows the number of robberies during a given month in 40 different towns of a state. Find the standard deviation based on this sample \(\begin{array}{|c|c|c|c|c|c|c|c|c|c|}\hline \text { Robberies } & {0} & {1} & {2} & {3} & {4} & {5} & {6} & {7} & {8} & {9} & {10} \\ \hline \text { Frequency } & {1} & {1} & {1} & {2} & {2} & {6} & {10} & {7} & {7} & {2} & {1} \\\ \hline\end{array}\)

Each time Mrs. Taggart fills the tank of her car, she estimates, from the number of miles driven and the number of gallons of gasoline needed to fill the tank, the fuel efficiency of her car, that is, the number of miles per gallon. The table shows the result of the last 20 times that she filled the car. a. Find the mean and the median fuel efficiency (miles per gallon) for her car. b. Find the percentile rank of 34 miles per gallon. $$ \begin{array}{|c|c|c|c|c|c|c|c|}\hline \text { Miles per } & {32} & {33} & {34} & {35} & {36} & {37} & {38} & {39} & {40} \\ \hline \text { Gallon } & {} & {} & {1} & {3} & {2} & {5} & {3} & {3} & {2} & {0} & {1} \\\ \hline\end{array} $$

Products often come with registration forms. One of the questions usually found on the registration form is household income. For a given product, the data below represents a random sample of the income (in thousands of dollars) reported on the registration form. Find the standard deviation based on this sample. $$\begin{array}{llllllllll}{38} & {40} & {26} & {42} & {39} & {25} & {40} & {40} & {39} & {36} \\ {46} & {41} & {43} & {47} & {49} & {43} & {39} & {35} & {43} & {37}\end{array}$$

In order to improve customer relations, an auto-insurance company surveyed 100 people to determine the length of time needed to complete a report form following an auto accident. The result of the survey is summarized in the following table showing the number of minutes needed to complete the form. Find the mean and median amount of time needed to complete the form. $$ \begin{array}{|c|c|c|c|c|c|c|c|c|c|}\hline \text { Minutes } & {26-30} & {31-35} & {36-40} & {41-45} & {46-50} & {51-55} & {56-60} & {61-65} & {66-70} \\\ \hline \text { Frequency } & {2} & {8} & {12} & {15} & {10} & {24} & {26} & {1} & {2} \\ \hline\end{array} $$