91Ó°ÊÓ

The state of California defines family income groups in terms of median county income as follows: Extremely low income: below \(30 \%\) of county median income Very low income: between \(30 \%\) and \(50 \%\) of county median income Low income: between \(50 \%\) and \(80 \%\) of county median income Moderate income: between \(80 \%\) and \(120 \%\) of county median income For San Luis Obispo County, the median income as of May 24,2016 for single person households was $$\$ 53,950$$ (www.slocounty.ca.gov/Assets/PL/Housing/AHS/AHS.pdf, August \(1,2016,\) retrieved April 19,2017\()\). a. Interpret the value of the median income for a singleperson household in San Luis Obispo County. b. Each of the following statements is incorrect. For each statement, use the given information to explain why it is incorrect. Statement 1: \(30 \%\) of the single-person households in San Luis Obispo County would be classified as extremely low income. Statement 2: More than \(50 \%\) of the single-person households in San Luis Obispo County would be classified as extremely low income or very low income. Statement 3 : There cannot be any single-person households in San Luis Obispo County that would be classified as having an income that was greater than those in the moderate income category.

The accompanying data are a subset of data read from a graph in the paper "Ladies First? A Field Study of Discrimination in Coffee Shops" (Applied Economics [April, 2008] ). The data are the waiting time (in seconds) between ordering and receiving coffee for 19 male customers at a Boston coffee shop. $$ \begin{array}{rrrrrrrrrr} 40 & 60 & 70 & 80 & 85 & 90 & 100 & 100 & 110 & 120 \\ 125 & 125 & 140 & 140 & 160 & 160 & 170 & 180 & 200 & \end{array} $$ Use these data to construct a boxplot. Write a few sentences describing the important characteristics of the boxplot.

The mean playing time for a large collection of compact discs is 35 minutes, and the standard deviation is 5 minutes. a. What value is 1 standard deviation above the mean? One standard deviation below the mean? What values are 2 standard deviations away from the mean? b. Assuming that the distribution of times is mound shaped and approximately symmetric, approximately what percentage of times are between 25 and 45 minutes? Less than 20 minutes or greater than 50 minutes? Less than 20 minutes? (Hint: See Example \(3.19 .\) )

The report "Who Borrows Most? Bachelor's Degree Recipients with High Levels of Student Debt" (trends .collegeboard.org/content/who-borrows-most-bachelors -degree-recipients-high-levels-student-debt-april-2010, retrieved April 20,2017 ) included the following percentiles for the amount of student debt for students graduating with a bachelor's degree in 2010: $$ \begin{array}{ll} \text { 10th percentile } & =\$ 0 & \text { 25th percentile }=\$ 0 \\ \text { 50th percentile } & =\$ 11,000 & \text { 75th percentile }=\$ 24,600 \\\ \text { 90th percentile } & =\$ 39,300 & \end{array} $$ For each of these percentiles, write a sentence interpreting the value of the percentile. (Hint: See Example 3.20.)

Suppose that your statistics professor returned your first midterm exam with only a \(z\) -score written on it. She also told you that a histogram of the scores was mound shaped and approximately symmetric. How would you interpret each of the following \(z\) -scores? a. 2.2 b. 0.4 c. 1.8 d. 1.0 e. 0

In a study investigating the effect of car speed on accident severity, the vehicle speed at impact was recorded for 5000 fatal accidents. For these accidents, the mean speed was 42 mph and the standard deviation was 15 mph. A histogram revealed that the vehicle speed distribution was mound shaped and approximately symmetric. a. Approximately what percentage of the vehicle speeds were between 27 and \(57 \mathrm{mph} ?\) b. Approximately what percentage of the vehicle speeds exceeded \(57 \mathrm{mph} ?\)

Suppose that your younger sister is applying to college and has taken the SAT exam. She scored at the 83 rd percentile on the verbal section of the test and at the 94 th percentile on the math section. Because you have been studying statistics, she asks you for an interpretation of these values. What would you tell her?

Suppose that the distribution of weekly water usage for single-family homes in a particular city is mound shaped and approximately symmetric. The mean is 1400 gallons, and the standard deviation is 300 gallons. a. What is the approximate value of the 16 th percentile? b. What is the approximate value of the median? c. What is the approximate value of the 84 th percentile?