In each of the following sentences, circle any letter that should be capitalized and draw a slash (\/) through any letter that should be lowercase. **Example 1**. $\text{\textcircled}{\text{{d}}}$id you ask $\text{\textcircled}{\text{{d}}}$r. fishbein or her ${\sout{\text{D}}}$ental ${\sout{\text{A}}}$ssistant about your toothache during your appointment last $\text{\textcircled}{\text{{f}}}$riday? “In case of an Emergency,” the notice read, “Please call $911$ to reach ems or the police.”

Study of why EMS workers leave the job. A study of fulltime emergency medical service (EMS) workers published in the Journal of Allied Health (Fall 2011) found that only about $3 \%$ leave their job in order to retire. (See Exercise $3.45$, p. 158.) Assume that the true proportion of all fulltime EMS workers who leave their job in order to retire is $p=.03$. In a random sample of 1,000 full-time EMS workers, let $\hat{p}$ represent the proportion who leave their job in order to retire. Describe the properties of the sampling distribution of $\hat{p}$.

A plane leaves Seattle, flies $85 \mathrm{mi}$ at $22^{\circ}$ north of east, and then changes direction to $48^{\circ}$ south of east. After flying at $115 \mathrm{mi}$ in this new direction, the pilot must make an emergency landing on a field. The Seattle airport facility dispatches a rescue crew.
($a$) In what direction and how far should the crew fly to go directly to the field? Use components to solve this problem.
($b$) Check the reasonableness of your answer with a careful graphical sum.

The following exercises describe apportionment problems for situations besides the House of Representatives. Do the following: a. Find the apportionment by Hamilton's method. b. Find the apportionment by Jefferson's method. c. Find the apportionment by Webster's method. d. Find the apportionment by the Hill-Huntington method. e. Compare the results of the various methods. A city plans to purchase 16 new emergency vehicles. They are to be apportioned among 485 members of the police department, 213 members of the fire department, and 306 members of the paramedic squad.

Potassium superoxide, $KO_2$, is employed in a self-contained breathing apparatus used by emergency personnel as a source of oxygen. The reaction is\

$4KO_2(s) + 2H_2O(l) \longrightarrow 4KOH(s) + 3O_2(g)$\

Say a self-contained breathing apparatus is charged with 750 g $KO_2$ and then is used to produce 195 g of oxygen. Was all of the $KO_2$ consumed in this reaction? If the $KO_2$ wasn’t all consumed, how much is left over and what mass of additional $O_2$ could be produced?

For many years Colonel John P. Stapp, USAF, held the world’s land speed record. He participated in studying whether a jet pilot could survive emergency ejection. On March $19$, $1954$, he rode a rocket-propelled sled that moved down a track at $632$ mi/h. He and the sled were safely brought to rest in $1.40$ s. Determine (a) the negative acceleration he experienced and (b) the distance he traveled during this negative acceleration, assumed to be constant.

A group of hikers is lost in a national park. Two ranger stations have received an emergency SOS signal from the hikers. Station B is 75 miles due east of station A. The bearing from station A to the signal is S 60° E and the bearing from station B to the signal is S 75° W. A rescue party is in the park 20 miles from station A at a bearing of S 80° E. Find the distance and the bearing the rescue party must travel to reach the lost hikers.

(a) A light-rail commuter train accelerates at a rate of 1.35 m/s². How long does it take to reach its top speed of 80.0 km/h, starting from rest? (b) The same train ordinarily decelerates at a rate of 1.65 m/s². How long does it take to come to a stop from its top speed? (c) In emergencies, the train can decelerate more rapidly, coming to rest from 80.0 km/h in 8.30 s. What is its emergency acceleration in meters per second squared?

Large stadiums rely on backup generators to provide electricity in the event of a power failure. Assume that emergency backup generators fail 22% of the times when they are needed (based on data from Arshad Mansoor, senior vice president with the Electric Power Research Institute). A stadium has three backup generators so that power is available if at least one of them works in a power failure. Find the probability of having at least one of the backup generators working given that a power failure has occurred. Does the result appear to be adequate for the stadium's needs?

While playing on her swing set, 10-year-old Yasmin falls and breaks her right leg. At the emergency room, the physician tells Yasmin's parents that the proximal end of the tibia, where the epiphysis meets the diaphysis, is fractured. The fracture is properly set and eventually heals. During a routine physical when she is 18 , Yasmin learns that her right leg is $2 cm$ shorter than her left, probably because of her accident. What might account for this difference?

Malcolm injured himself after trying to break his fall with outstretched arms. The emergency room physician took one look at his shoulder and saw that Malcolm had a broken clavicle (and no other injury). Describe the position of Malcolm’s shoulder. What part of the clavicle was most likely broken? Malcolm was worried about injury to the main blood vessels to his arm (the subclavian vessels), but he was told such injury was unlikely. Why could the doctor predict this?

Myrna White is a mobile housekeeper. The price for a standard house cleaning is $150 and takes 5 hours. Each worker is paid$25/hour, uses $15 of materials and$0.50 per mile to use their own vehicle to travel from job to job. The average job is 5 miles. Arniz Meyroyan has a family reunion at her house and needs her house freshened up. She offers $75 for this emergency tidy-up service. This service includes vacuuming and cleaning floors, dusting, and cleaning the bathrooms. Only$5 of materials would be used.

Myrna White is a mobile housekeeper. The price for a standard house cleaning is $150 and takes 5 hours. Each worker is paid$25/hour, uses $15 of materials and$0.50 per mile to use their own vehicle to travel from job to job. The average job is 5 miles. Arniz Meyroyan has a family reunion at her house and needs her house freshened up. She offers $75 for this emergency tidy-up service. This service includes vacuuming and cleaning floors, dusting, and cleaning the bathrooms. Only$5 of materials would be used.

B. If a $25 surcharge was included to make the price of$100 how would the differential income change?

(a) Recall Which amendment guaranteed African Americans the right to vote: the Thirteenth, Fourteenth, or Fifteenth?

(b) Apply Information How did each of these three amendments help to expand democracy?

Let X denote the number of times a certain numerical control machine will malfunction: 1, 2, or 3 times on any given day. Let Y denote the number of times a technician is called on an emergency call. Their joint probability distribution is given as

$$\begin{matrix} & & & x & \\ \hline & & 1 & 2 & 3 \\ & 1 & 0.05 & 0.05 & 0.10 \\ y & 3 & 0.05 & 0.10 & 0.35 \\ & 5 & 0.00 & 0.20 & 0.10 \end{matrix}$$

(a) Evaluate the marginal distribution of X. (b) Evaluate the marginal distribution of Y. (c) Find P(Y=3|X=2).