Provide examples of four situations in which there is a limited, or finite, waiting line.

Which of the following situations does not involve potential energy being changed into kinetic energy? a. an apple falling from a tree b. shooting a dart from a spring-loaded gun c. pulling back on the string of a bow d. a creek flowing downstream

Indicate which of the following situations involve sampling from a finite population and which involve sampling from an infinite population. In cases where the sampled population is finite, describe how you would construct a frame.

Obtain a sample of the orders that are processed by a mail-order firm.

Calculate the percentage of the population sampled and the finite population correction factor for each of the following situations: $n=1,000, N=5,000$

Indicate which of the following situations involve sampling from a finite population and which involve sampling from an infinite population. In cases where the sampled population is finite, describe how you would construct a frame.

Obtain a sample of licensed drivers in the state of New York.

Finite vs. Infinite Populations. Indicate which of the following situations involve sampling from a finite population and which involve sampling from an infinite population. In cases where the sampled population is finite, describe how you would construct a frame.

c. Select a sample of cars crossing the Golden Gate Bridge on a typical weekday.

Finite vs. Infinite Populations. Indicate which of the following situations involve sampling from a finite population and which involve sampling from an infinite population. In cases where the sampled population is finite, describe how you would construct a frame.

e. Select a sample of the orders being processed by a mail-order firm.

A student government organization is interested in estimating the proportion of students who favor a mandatory “pass-fail” grading policy for elective courses. Alist of names and addresses of the 645 students enrolled during the current quarter is available from the registrar’s office. Using three-digit random numbers in row 10 of Table below and moving across the row from left to right, identify the first 10 students who would be selected using simple random sampling. The three-digit random numbers begin with 816, 283, and 610.

$$\begin{matrix} \text{63271} & \text{59986} & \text{71744} & \text{51102} & \text{15141} & \text{80714} & \text{58683} & \text{93108} & \text{13554} & \text{79945}\\ \text{88547} & \text{9896} & \text{95436} & \text{79115} & \text{8303} & \text{1041} & \text{20030} & \text{63754} & \text{8459} & \text{28364}\\ \text{55957} & \text{57243} & \text{83865} & \text{9911} & \text{19761} & \text{66535} & \text{40102} & \text{26646} & \text{60147} & \text{15702}\\ \text{46276} & \text{87453} & \text{44790} & \text{67122} & \text{45573} & \text{84358} & \text{21625} & \text{16999} & \text{13385} & \text{22782}\\ \text{55363} & \text{7449} & \text{34835} & \text{15290} & \text{76616} & \text{67191} & \text{12777} & \text{21861} & \text{68689} & \text{3263}\\ \text{69393} & \text{92785} & \text{49902} & \text{58447} & \text{42048} & \text{30378} & \text{87618} & \text{26933} & \text{40640} & \text{16281}\\ \text{13186} & \text{29431} & \text{88190} & \text{4588} & \text{38733} & \text{81290} & \text{89541} & \text{70290} & \text{40113} & \text{8243}\\ \text{17726} & \text{28652} & \text{56836} & \text{78351} & \text{47327} & \text{18518} & \text{92222} & \text{55201} & \text{27340} & \text{10493}\\ \text{36520} & \text{64465} & \text{5550} & \text{30157} & \text{82242} & \text{29520} & \text{69753} & \text{72602} & \text{23756} & \text{54935}\\ \text{81628} & \text{36100} & \text{39254} & \text{56835} & \text{37636} & \text{2421} & \text{98063} & \text{89641} & \text{64953} & \text{99337}\\ \text{84649} & \text{48968} & \text{75215} & \text{75498} & \text{49539} & \text{74240} & \text{3466} & \text{49292} & \text{36401} & \text{45525}\\ \text{63291} & \text{11618} & \text{12613} & \text{75055} & \text{43915} & \text{26488} & \text{41116} & \text{64531} & \text{56827} & \text{30825}\\ \text{70502} & \text{53225} & \text{3655} & \text{5915} & \text{37140} & \text{57051} & \text{48393} & \text{91322} & \text{25653} & \text{6543}\\ \text{6426} & \text{24771} & \text{59935} & \text{49801} & \text{11082} & \text{66762} & \text{94477} & \text{2494} & \text{88215} & \text{27191}\\ \text{20711} & \text{55609} & \text{29430} & \text{70165} & \text{45406} & \text{78484} & \text{31639} & \text{52009} & \text{18873} & \text{96927}\\ \text{41990} & \text{70538} & \text{77191} & \text{25860} & \text{55204} & \text{73417} & \text{83920} & \text{69468} & \text{74972} & \text{38712}\\ \text{72452} & \text{36618} & \text{76298} & \text{26678} & \text{89334} & \text{33938} & \text{95567} & \text{29380} & \text{75906} & \text{91807}\\ \text{37042} & \text{40318} & \text{57099} & \text{10528} & \text{9925} & \text{89773} & \text{41335} & \text{96244} & \text{29002} & \text{46453}\\ \text{53766} & \text{52875} & \text{15987} & \text{46962} & \text{67342} & \text{77592} & \text{57651} & \text{95508} & \text{80033} & \text{69828}\\ \text{90585} & \text{58955} & \text{53122} & \text{16025} & \text{84299} & \text{53310} & \text{67380} & \text{84249} & \text{25348} & \text{4332}\\ \text{32001} & \text{96293} & \text{37203} & \text{64516} & \text{51530} & \text{37069} & \text{40261} & \text{61374} & \text{5815} & \text{6714}\\ \text{62606} & \text{64324} & \text{46354} & \text{72157} & \text{67248} & \text{20135} & \text{49804} & \text{9226} & \text{64419} & \text{29457}\\ \text{10078} & \text{28073} & \text{85389} & \text{50324} & \text{14500} & \text{15562} & \text{64165} & \text{6125} & \text{71353} & \text{77669}\\ \text{91561} & \text{46145} & \text{24177} & \text{15294} & \text{10061} & \text{98124} & \text{75732} & \text{815} & \text{83452} & \text{97355}\\ \text{13091} & \text{98112} & \text{53959} & \text{79607} & \text{52244} & \text{63303} & \text{10413} & \text{63839} & \text{74762} & \text{50289}\\ \end{matrix}$$

Bill Youngdahl has been collecting data at the TU student grill. He has found that, between 5:00 P.M. and 7:00 P.M., students arrive at the grill at a rate of 25 per hour (Poisson distributed) and service time takes an average of 2 minutes (negative exponential distribution). There is only 1 server, who can work on only $l$ order at a time.

Suppose a second server is added and the 2 servers act independently, with each taking an average of 2 minutes. What would be the average time a student is in the system?

Bill Youngdahl has been collecting data at the TU student grill. He has found that, between 5:00 P.M. and 7:00 P.M., students arrive at the grill at a rate of 25 per hour (Poisson distributed) and service time takes an average of 2 minutes (negative exponential distribution). There is only 1 server, who can work on only $l$ order at a time.

Suppose that a second server can be added to team up with the first (and, in effect, act as 1 faster server). This would reduce the average service time to 90 seconds. How would this affect the average time a student is in the grill area?

Bill Youngdahl has been collecting data at the TU student grill. He has found that, between 5:00 P.M. and 7:00 P.M., students arrive at the grill at a rate of 25 per hour (Poisson distributed) and service time takes an average of 2 minutes (negative exponential distribution). There is only 1 server, who can work on only $l$ order at a time.

What is the average time a student is in the grill area?

Bill Youngdahl has been collecting data at the TU student grill. He has found that, between 5:00 P.M. and 7:00 P.M., students arrive at the grill at a rate of 25 per hour (Poisson distributed) and service time takes an average of 2 minutes (negative exponential distribution). There is only 1 server, who can work on only $l$ order at a time.

What is the average number of students in line?

Discuss the likely outcome of a waiting line system where $\mu>\lambda$ but only by a tiny amount (e.g., $\mu=4.1, \lambda=4$ ).

Beate Klingenberg manages a Poughkeepsie. New York, movie theater complex called Cinema 8. Each of the eight auditoriums plays a different film; the schedule staggers starting times to avoid the large crowds that would occur if all four movies started at the same time. The theater has a single ticket booth and a cashier who can maintain an average service rate of 280 patrons per hour. Service times are assumed to follow a negative exponential distribution. Arrivals on a normally active day are Poisson distributed and average 210 per hour.

To determine the efficiency of the current ticket operation, Beate wishes to examine several queue-operating characteristics.

What is the probability that there are more than two people in the system? More than three people? More than four?