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 $P(\hat{p}>.025)$. Interpret this result.

Suppose an emergency van has a single-tone siren with the pitch of the musical note $\mathrm{G}$. If the van is traveling at $80 \mathrm{mph}$ approaching a standing observer, name the pitch the observer hears (rounded to the nearest tenth) and the musical note closest to that pitch.

Pitch of an Octave of Musical Notes in Hertz $(\mathrm{Hz})$

$$\begin{aligned} &\begin{array}{c|c} \hline Note & Pitch \\ \hline Middle\ C & 261.63 \\ \hline D & 293.66 \\ \hline E & 329.63 \\ \hline F & 349.23 \\ \hline G & 392.00 \\ \hline A & 440.00 \\ \hline B & 493.88 \\ \hline \end{array} \end{aligned}$$

Study of why EMS workers leave the job. An investigation into why emergency medical service (EMS) workers leave the profession was published in the Journal of Allied Health (Fall 2011). The researchers surveyed a sample of 244 former EMS workers, of which 127 were fully compensated while on the job, 45 were partially compensated, and 72 had noncompensated volunteer positions. The numbers of EMS workers who left because of retirement were 7 for fully compensated workers, 11 for partially compensated workers, and 10 for noncompensated volunteers. One of the 244 former EMS workers is selected at random. Find the probability that the former EMS worker was not fully compensated while on the job.

According to Brighton Webs LTD, a British company that specializes in data analysis, the arrival time of requests to a Web server within each hour can be modeled by a uniform distribution ( www.brighton-webs. co.uk ). Specifically, the number of seconds x from the start of the hour that the request is made is uniformly distributed between 0 and 3,600 seconds. Find the probability that a request is made to a Web server sometime during the last 15 minutes of the hour.

You learned that Brighton Webs LTD modeled the arrival time of requests to a Web server within each hour using a uniform distribution. Specifically, the number of seconds x from the start of the hour that the request is made is uniformly distributed between 0 and 3,600 seconds. In a random sample of $n = 60$ Web server requests, let $\bar{x}$ represent the sample mean number of seconds from the start of the hour that the request is made. a. Find $E(\bar{x})$ and interpret its value. b. Find $\operatorname{Var}(\bar{x})$. c. Describe the shape of the sampling distribution of $\bar{x}$. d. Find the probability that $\bar{x}$ is between 1,700 and 1,900 seconds. e. Find the probability that $\bar{x}$ exceeds 2,000 seconds.

Study of why EMS workers leave the job. An investigation into why emergency medical service (EMS) workers leave the profession was published in the Journal of Allied Health (Fall 2011). The researchers surveyed a sample of 244 former EMS workers, of which 127 were fully compensated while on the job, 45 were partially compensated, and 72 had noncompensated volunteer positions. The numbers of EMS workers who left because of retirement were 7 for fully compensated workers, 11 for partially compensated workers, and 10 for noncompensated volunteers. One of the 244 former EMS workers is selected at random. Find the probability that the former EMS worker was either fully compensated while on the job or left due to retirement.

Study of why EMS workers leave the job. An investigation into why emergency medical service (EMS) workers leave the profession was published in the Journal of Allied Health (Fall 2011). The researchers surveyed a sample of 244 former EMS workers, of which 127 were fully compensated while on the job, 45 were partially compensated, and 72 had noncompensated volunteer positions. The numbers of EMS workers who left because of retirement were 7 for fully compensated workers, 11 for partially compensated workers, and 10 for noncompensated volunteers. One of the 244 former EMS workers is selected at random. Find the probability that the former EMS worker was fully compensated while on the job.

Study of why EMS workers leave the job. Refer to the Journal of Allied Health (Fall 2011) study of why emergency medical service (EMS) workers leave the profession, Exercise $3.45$ (p. 158). Recall that in a sample of 244 former EMS workers, 127 were fully compensated while on the job, 45 were partially compensated, and 72 had noncompensated volunteer positions. Also, the numbers of EMS workers who left because of retirement were 7 for fully compensated workers, 11 for partially compensated workers, and 10 for noncompensated volunteers. Given that the former EMS worker was fully compensated while on the job, estimate the probability that the worker left the EMS profession due to retirement.

Sean and Mason run out of gas while fishing from their boat in the bay. They set off an emergency flare with an initial vertical velocity of 30 meters per second. The height of the flare in meters can be modeled by $h(t)=-5 t^2+30 t$, where t represents the number of seconds after launch.

Sean wants to know how high the flare will reach above the surface of the water.

a. Write the function in vertex form, factoring so the coefficient of $t^2$ is 1 .

b. Complete the square using the vertex form of the function.

c. How high will the flare reach?

Large stadiums rely on backup generators to provide electricity in the event of a power failure. Assume that emergency backup generators fail 22% of the times when they are needed (based on data from Arshad Mansoor, senior vice president with the Electric Power Research Institute). A stadium has three backup generators so that power is available if at least one of them works in a power failure. Find the probability of having at least one of the backup generators working given that a power failure has occurred. Does the result appear to be adequate for the stadium's needs?

(a) A light-rail commuter train accelerates at a rate of 1.35 m/s². How long does it take to reach its top speed of 80.0 km/h, starting from rest? (b) The same train ordinarily decelerates at a rate of 1.65 m/s². How long does it take to come to a stop from its top speed? (c) In emergencies, the train can decelerate more rapidly, coming to rest from 80.0 km/h in 8.30 s. What is its emergency acceleration in meters per second squared?

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 vehicle is stuck on the railroad tracks as a 430,000 lb locomotive is approaching with a speed of 75 mph. As soon as the problem is detected, the locomotive’s emergency brakes are activated, locking the wheels and causing the locomotive to slide. If the coefficient of kinetic friction between the locomotive and the track is 0.45, what is the minimum distance d at which the brakes must be applied to avoid a collision? What would that distance be if instead of a locomotive, there was a $30 \times 106 lb$ train? Treat the locomotive and the train as particles, assume that the railroad tracks are rectilinear and horizontal, and note that only the locomotive’s brakes are applied.

A driver makes an emergency stop and inadvertently locks up the brakes of the car, which skids to a stop on dry concrete. Consider the effect of heavy rain on this scenario. Using the values in Table 1, determine how much farther the car would skid (expressed as a percentage of the dry-weather skid) if the concrete were wet instead. What does this question imply about driving safely?

Table 1 Coeffi cients of Kinetic Friction for Rubber on Concrete