Heart failure is due to either natural occurrences (87%) or outside factors (13%). Outside factors are related to induced substances or foreign objects. Natural occurrences are caused by arterial blockage, disease, and infection. Suppose that 20 patients will visit an emergency room with heart failure. Assume that causes of heart failure between individuals are independent. (a) What is the probability that three individuals have conditions caused by outside factors? (b) What is the probability that three or more individuals have conditions caused by outside factors? (c) What are the mean and standard deviation of the number of individuals with conditions caused by outside factors?

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 $\hat{p}$.

While you are talking with your friend at an expensive restaurant, she quickly stops in midswallow and looks panicked. When you ask what is wrong, she indicates that she can’t speak and runs toward the restroom. What should you do? Suppose that your first aid does not work---what procedure might emergency medical personnel use to help your her?

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.

The frequency table summarizes the distribution of time that 140 patients at the emergency room of a small-city hospital waited to receive medical attention during the last month.

$$\begin{array}{lr} \hline \text { Waiting time } & \text { Frequency } \\ \hline \text { Less than } 10 \text { minutes } & 5 \\ \text { At least } 10 \text { but less than } 20 \text { minutes } & 24 \\ \text { At least } 20 \text { but less than } 30 \text { minutes } & 45 \\ \text { At least } 30 \text { but less than } 40 \text { minutes } & 38 \\ \text { At least } 40 \text { but less than } 50 \text { minutes } & 19 \\ \text { At least } 50 \text { but less than } 60 \text { minutes } & 7 \\ \text { At least } 60 \text { but less than } 70 \text { minutes } & 2 \\ \hline \end{array}$$

Which of the following represents possible values for the median and IQR of waiting times for the emergency room last month? (a) median = 27 minutes and IQR = 15 minutes (b) median = 28 minutes and IQR = 25 minutes (c) median = 31 minutes and IQR = 35 minutes (d) median = 35 minutes and IQR = 45 minutes (e) median = 45 minutes and IQR = 55 minutes

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.

Desert Samaritan Hospital, in Mesa, Arizona, keeps records of emergency room traffic. Those records reveal that the times between arriving patients have a special type of reverse-J-shaped distribution called an exponential distribution. The records also show that the mean time between arriving patients is 8.7 minutes. a. Simulate four random samples of 75 interarrival times each. b. Perform a correlation test for normality on each sample in part (a). Use $\alpha=0.05$. c. Are the conclusions in part (b) what you expected? Explain your answer.

The waiting time until service at a hospital emergency department is modeled with the pdf $f (x) = \frac{1}{9} x \quad 0<x<3$ hours and $f (x) = \frac{2}{3}-\frac{1}{9} x \quad 3<x<6.$ Determine the following: (a) Probability the wait is less than 4 hours (b) Probability the wait is more than 5 hours (c) Probability the wait is less than or equal to 30 minutes (d) Waiting time that is exceeded by only 10% of patients (e) Mean waiting time

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?

A nuclear reactor is equipped with two independent automatic shutdown systems to shut down the reactor when the core temperature reaches the danger level. Neither system is perfect. System A shuts down the reactor 90% of the time when the danger level is reached. System B does so 80% of the time. The reactor is shut down if either system works.

Now simulate 100 trials of the reactor's response to an emergency of this kind. Estimate the probability that it will shut down. This probability is higher than the probability that either system working alone will shut down the reactor.

The probability that a call to an emergency help line is answered in less than 15 seconds is 0.85. Assume that all calls are independent. (a) What is the probability that exactly 7 of 10 calls are answered within 15 seconds? (b) What is the probability that at least 16 of 20 calls are answered in less than 15 seconds? (c) For 50 calls, what is the mean number of calls that are answered in less than 15 seconds? (d) Repeat parts (a)–(c) using the normal approximation.

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.?

In an emergency, it is sometimes the practice of medical professionals to immerse a patient who suffers from heat stroke in an ice bath, a mixture of ice and water in equilibrium at $0 ^ { \circ } \mathrm { C }$, in order to reduce body temperature is $40.8 ^ { \circ } \mathrm { C }$ must have her temperature reduced to the normal range, how much heat must be removed? (b) If she is placed in a bath containing 7.5 kg of ice, will there be ice remaining in the bath when her body temperature is $37.0 ^ { \circ } \mathrm { C } ?$ If so, how much? If not, what will the final water temperature be?

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