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.

Five-year-old Amy wakes her parents up at 3 AM crying and complaining of a sore neck, a severe headache, and feeling sick to her stomach. She has a temperature of $40^{\circ} \mathrm{C}$ $\left(104^{\circ} \mathrm{F}\right)$ and hides her eyes, saying that the lights are too bright. The emergency physician suspects meningitis and performs a lumbar tap. Using your knowledge of neuroanatomy, explain into which space and at what level of the vertebral column the needle will be inserted to perform this test. Which fluid is being obtained and why?

A plane traveling horizontally at 80 m/s} over flat ground at an elevation of 3000 m releases an emergency packet. The trajectory of the packet is given by

$$x=80 t, \quad y=-4.9 t^2+3000, \quad \text { for } t \geq 0,$$

where the origin is the point on the ground directly beneath the plane at the moment of the release. Graph the trajectory of the packet and find the coordinates of the point where the packet lands.

Determine whether the two random variables, given in the following way, are dependent or independent. 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

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

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.

An 8-year-old child is being admitted to the hospital from the emergency department with an injury from falling off her bicycle. Which of the following will most help her adjust to the hospital?

1. Explain hospital routines such as mealtimes to her.
2. Use terms such as “honey” and “dear” to show a caring attitude.
3. Explain when her parents can visit and why siblings cannot come to see her.
4. Since she is young, orient her parents to her room and hospital facility.

Three-year-old C.E. is admitted to the Emergency Department (ED) fast track clinic. Her mother tells the nurse that C.E. has had a low-grade fever for $2$ days and is complaining of ear pain and a sore throat. Mrs. E. states that C.E.'s appetite has been “off,” but she has been drinking and using the bathroom as usual.

As you get C.E. settled in the exam room, what routine information regarding risk factors for otitis media (OM) would you want to obtain from Mrs. E.?

(Use Excel) Color coding is often used in manufacturing operations to display production status or to identify/prioritize materials. For example, suppose "green" status indicates that an assembly line is operating normally, "yellow" indicates it is down waiting on personnel for set up or repair, "blue" indicates it is down waiting on materials to be delivered, and "red" indicates an emergency condition. Management has set realistic goals whereby the assembly line should be operating normally 80% of the time, waiting on personnel 9% of the time, waiting on materials $9 \%$ of the time, and in an emergency condition 2% of the time. Based on $250$ recent status records, the status was green $185$ times, yellow $24$ times, blue $32$ times, and red $9$ times.

a. State the appropriate null and alternative hypotheses to test if the proportions of assembly line statuses differ from the goals set by management.

b. Calculate the value of the test statistic.

c. Use Excel's CHISQ.DIST.RT function to calculate the $p$-value.

d. Are management's goals being met at $\alpha=0.05$ ? Will your conclusion change at $\alpha=0.01$ ?

B.L., 17, had a compression fracture at the C5-C6 after jumping into a river from a bridge and slamming into a submerged rock. Fortunately, she was saved by a companion who had first-aid expertise and worked to limit any collateral damage. B.L. was unable to move her limbs, feel touch, or have reflexes in her limbs when she arrived at the emergency room. Describe why it is impossible to determine the entire amount of lasting damage during this initial time frame.

While playing on her swing set, 10-year-old Rebecca falls and breaks her right leg. At the emergency room, the doctor tells her 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, Rebecca learns that her right leg is 2.54 cm (1 in.) shorter than her left. What might account for this difference?

Ambulance response time. Geographical Analysis (Jan. 2010) presented a study of emergency medical service (EMS) ability to meet the demand for an ambulance. In one example, the researchers presented the following scenario. An ambulance station has one vehicle and two demand locations, $\mathrm{A}$ and $\mathrm{B}$. The probability that the ambulance can travel to a location in under 8 minutes is $.58$ for location $\mathrm{A}$ and $.42$ for location $\mathrm{B}$. The probability that the ambulance is busy at any point in time is $.3$. Find the probability that EMS can meet the demand for an ambulance at location B.

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

Three-year-old C.E. is admitted to the Emergency Department (ED) fast track clinic. Her mother tells the nurse that C.E. has had a low-grade fever for $2$ days and is complaining of ear pain and a sore throat. Mrs. E. states that C.E.'s appetite has been “off,” but she has been drinking and using the bathroom as usual.

Mrs. E. is given a new prescription for azithromycin (Zithromax) PO $160$ mg qd $\times$ $5$ days.

5. Azithromycin is dispensed $200$ mg/$5$ mL. Calculate the dosage for Mrs. E. to administer to C.E

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?