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.

A patient is evaluated in the emergency department after causing an automobile accident while being under the influence of alcohol. While assessing the patient, which statement would be the most therapeutic?

1. “Why did you drive after you had been drinking?”
2. “We have multiple patients to see tonight as a result of this accident.”
3. “Tell me what happened before, during, and after the automobile accident tonight.”
4. “It will be okay. No one was seriously hurt in the accident.”

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.

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 the causes and ways in which B.L.'s ability to breathe may be hampered at any time.

As a young design engineer you are asked to design an emergency braking parachute system for use with a military aircraft of mass 9500 kg. The plane lands at 350 km/hr, and the parachute system alone must slow the airplane to 100 km/hr in less than 1200 m. Find the minimum diameter required for a single parachute, and for three noninterfering parachutes. Plot the airplane speed versus distance and versus time. What is the maximum “g-force” experienced?

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?

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.

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.

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.

After a heavy meal rich with fried foods, Debby Collins, an overweight 45-year-old woman, was rushed to the emergency room with severe spasmodic pains in her epigastric region that radiated to the right side of her rib cage. She indicated that the attack came on suddenly, and her abdomen was found to be tender to the touch and somewhat rigid. What do you think is this patient's problem and why is her pain discontinuous (colicky)? What are the treatment options and what might happen if the problem is not resolved?

A recently graduated mechanical engineer wants to build a reserve fund as a safety net to pay his expenses in the unlikely event that an unexpected emergency arises. His aim is to have $45,000 developed over the next 3 years, with the proviso that the amount must have the same purchasing power as$45,000 today. If the expected market rate on investments is 8% per year and inflation is averaging 2% per year, find the annual amount necessary to meet his goal.

A traffic engineer determines that the number of cars passing through a certain intersection each week can be modeled by $C(x)=0.02x^3+0.4x^2+0.2x+35$, where x Is the number of weeks since the survey began. A new road has just opened that affects the traffic at that intersection. Let $N(x)=C(x)+200$.
Emergency roadwork temporarily closes off most of the traffic to this intersection. Write a function R(x) that could model the effect on C(x) Explain how the graph of C(x) might be transformed into R{x).

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.

You are driving a car when a deer suddenly darts across the road in front of you. Your brain registers the emergency and sends a signal to your foot to hit the brake. The car travels a reaction distance D, in feet, during this time, where D is a function of the speed r, in miles per hour, that the car is traveling when you see the deer, given by $D(r)=\frac{11 r+5}{10}.$ Find the inverse and explain what it represents. Is the inverse a function?