(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 $\alpha=0.01$ ?

Doctors treated a patient at an emergency room from 2:00 P.M. to 7:00 P.M. The patient’s blood oxygen level L (in percent) during this time period can be modeled by $L=-0.270 t^{2}+3.59 t+83.1, \quad 2 \leq t \leq 7$ where t represents the time of day, with t=2 corresponding to 2:00 P.M. Use the model to estimate the time (rounded to the nearest hour) when the patient’s blood oxygen level was 93%.

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

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.”

USA Today reporter Paul Wiseman described the old rules for the three-digit telephone area codes by writing about "possible area codes with 1 or 0 in the second digit. (Excluded: codes ending in 00 or 11, for toll-free calls, emergency services, and other special uses.)" Codes beginning with 0 or 1 should also be excluded. How many different area codes were possible under these old rules?

A man was driving to work when his car was hit broadside by a car that ran a red light. When freed from the wreckage, the man was deeply cyanotic, and his breathing had stopped. His heart was still beating, but his pulse was fast and thready. His head was cocked at a peculiar angle, and the emergency personnel said he seemed to have a fracture at the level of vertebra C2
Define cyanosis and indicate why the man was cyanotic

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?

The Fugitive Slave Act made it a federal crime to A. assist runaway slaves. B. give jobs to freedmen . C. sell slaves in the North. D. allow African Americans to vote.

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.

While playing on her swing set, 10-year-old Yasmin falls and breaks her right leg. At the emergency room, the physician tells Yasmin's 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 , Yasmin learns that her right leg is $2 cm$ shorter than her left, probably because of her accident. What might account for this difference?

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

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 of having a working generator in the event of a power outage. Is that probability high enough for the hospital?

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. Describe the properties of the sampling distribution of $\hat{p}$.