The following table, reproduced from earlier exercise, gives the probability distribution of the number of patients who enter Millard Fellmore Memorial Hospital's emergency room in a given hour.

$$\begin{array}{l|ccccccc} \hline \text { Patients per hour } & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline \text { Probability } & .2725 & .3543 & .2303 & .0998 & .0324 & .0084 & .0023 \\ \hline \end{array}$$

Calculate this probability distribution's mean and standard deviation.

The temperature T (in degrees Fahrenheit) of a patient t hours after arriving at the emergency room of a hospital at 10:00 P.M. is given by $T(t)=98.6+4 \cos \frac{\pi t}{36}, \quad 0 \leq t \leq 18$. Find the patient’s temperature at (a) 10:00 P.M., (b) 4:00 A.M., and (c) 10:00 A.M. (d) At what time do you expect the patient’s temperature to return to normal? Explain your reasoning.

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

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.

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 treatment do you anticipate?

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.

(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 $\alpha=0.01$ ?

J.R. is a 28-year-old man who was doing home repairs. He fell from the top of a 6-foot stepladder, striking his head on a large rock. He experienced a momentary loss of consciousness. By the time his neighbour got to him, he was conscious but bleeding profusely from a laceration over the right temporal area. The neighbour drove him to the emergency department of your hospital. As the nurse, you immediately apply a cervical collar, lay him on a stretcher, and take J.R. to a treatment room.
What steps will you take to assess J.R.?

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.

Forty patients were asked how many minutes they had to wait in an emergency department before they were seen by a doctor. The results are below. Construct a frequency distribution table using five classes.
32 40 66 51 28 35 30 45 49 33
37 41 56 43 59 60 32 48 56 55
50 29 44 54 64 65 49 34 39 30
36 34 47 52 43 47 58 31 61 29

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

The flywheel of an old steam engine is a solid homogeneous metal disk of mass $M=120 \mathrm{~kg}$ and radius $R=80.0 \mathrm{~cm}$. The engine rotates the wheel at 500 . rpm. In an emergency, to bring the engine to a stop, the flywheel is disengaged from the engine and a brake pad is applied at the edge to provide a radially inward force $F=100$. N. If the coefficient of kinetic friction between the pad and the flywheel is $\mu_{\mathrm{k}}=0.200$, how many revolutions does the flywheel make before coming to rest? How long does it take for the flywheel to come to rest? Calculate the work done by the torque during this time.

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.

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?