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.

Evaluate the expression to complete the table. "

$$\begin{matrix} & \text{Mammals with the Longest Tails}\\ \text{Mammal} & \text{Expression} & \text{Tail Length}\\ \text{African elephant} & \mathrm{6 \times ( 72 \div 8 ) - 3} & \text{\_\_\_\_\_}\\ \end{matrix}$$

"

$$\left. \begin{array} { l } { \text { . The interval between patient arrivals in an emergency room } } \\ { \text { is a random variable with exponential density function } p ( t ) = } \\ { 0.125 e ^ { - 0.125 t } ( t \text { in minutes). What is the average time between pa- } } \\ { \text { tient arrivals? What is the probability of two patients arriving within } 3 } \\ { \text { min of each other? } } \end{array} \right.$$

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.

Review the events listed under "Migration and Settlement" on the thematic timeline on page 237, and then discuss how southern expansion, the end of the Atlantic slave trade in 1808, and the subsequent rise of the internal slave trade affected the experiences and identities of the African American population.

Hos pitals typically req uire backup generators to provide electricity in the event of a power outage. Assume that emergency backup generato rs fai l 22% of the times when they are needed (based on data from Arshad Mansoor, senior vice president with the Electric Power Research In stitute). A hospital has two backup generators so that power is avail able if one of them fails during a power outage. Find the probability that both generators fail during a power outage.

You are working in the emergency department (ED) of a community hospital when the ambulance arrives with A.N., an $18$-year-old woman who was caught in a house fire. She was sleeping when the fire started and managed to make her way out of the house through thick smoke. The emergency medical system crew initiated humidified oxygen at $15 \mathrm{~L} / \mathrm{min}$ per nonrebreather mask and started a $16$-gauge IV with lactated Ringer's solution. On arrival to the ED, her vital signs are $100/66, 125, 34$, $\mathrm{SaO}_2 93 \%$. An additional $16$-gauge IV is inserted. She appears anxious and in pain.

Eighteen hours after the injury, the NAP reports these vital signs for A.N. and states that the urine output for the past hour was $20$ mL.

$$\begin{aligned} &\text { Vital Signs }\\ &\begin{array}{ll} \text { Blood pressure } & 90 / 50 \mathrm{~mm} \mathrm{Hg} \\ \text { Heart rate } & 110 \text { beats } / \mathrm{min} \\ \text { Respiratory rate } & 24 \text { breaths } / \mathrm{min} \end{array} \end{aligned}$$

What do you suspect is occurring, and why does this concern you?

The frequency distribution shows the number of medical tests conducted on 30 randomly selected emergency room patients.

If a patient is selected at random, find these probabilities:

a. The patient had exactly 3 tests done. b. The patient had at most 2 tests done. c. The patient has 1 or 2 tests done. d. The patient had fewer than 3 tests done. e. The patient had at least 3 tests done.

T.W. is a 22-year-old man who fell SO feet from a chairlift while skiing and landed on hard-packed snow. He is now at the emergency department (ED) with a suspected TS-T6 fracture with paraplegia.
Insert Foley catheter
ECG monitoring
Immobilize the cervical spine
Oxygen at 4 L per nasal cannula
Initiate two large bore IVs
Neurologic assessment every hour
Apply warming blankets as needed
Describe a plan for implementing these physician's orders

A hiker caught in a thunderstorm loses heat when her clothing becomes wet. She is packing emergency rations that if completely metabolized will release $35 \mathrm{~kJ}$ of heat per gram of rations consumed. How much rations must the hiker consume to avoid a reduction in body temperature of $2.5 \mathrm{~K}$ as a result of heat loss? Assume the heat capacity of the body equals that of water and that the hiker weighs $51 \mathrm{~kg}$. State any additional assumptions.

You are on duty in the emergency department (ED) when a "code blue" is called. As the code nurse, you grab the crash cart and run to the code, which is in the employee lounge of the operating room. On the couch, you find a nurse, Z.H., unconscious, dusky, and barely breathing
Z.H.'s respiratory rate is 8 and shallow. The respiratory therapist intubates her and continues to ventilate her manually. You attach ECG leads to her chest and find the results shown in the figure. What is your interpretation of Z.H.'s rhythm?

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. Compute $P(\hat{p}<.05)$. Interpret this result.

An emergency braking parachute system on a military aircraft consists of a large parachute of diameter 6 m. If the airplane mass is 8500 kg, and it lands at 400 km/hr, find the time and distance at which the airplane is slowed to 100 km/hr by the parachute alone. Plot the aircraft speed versus distance and versus time. What is the maximum “g-force” experienced? An engineer proposes that less space would be taken up by replacing the large parachute with three noninterfering parachutes each of diameter 3.75 m. What effect would this have on the time and distance to slow to 100 km/hr?

Define Type I and Type II error for each scenario, and identify the cost(s) of each type of error.

Approaching O'Hare for landing, a British Air flight from London has been in a holding pattern for $45$ minutes due to bad weather. Landing is expected within $15$ minutes. The flight crew could declare an emergency and land immediately, but an FAA investigation would be launched and other flights might be endangered. The null hypothesis is that there is enough fuel to stay aloft for $15$ more minutes.