Assume that the arrival of airplanes at a one-runway airport is a Poisson distribution with a mean rate of 8 planes per hour. The landing time (service time, not service rate which would be planes/min) is an exponential distribution with a mean of 5 minutes per plane. What is the mean number of planes in a holding (planes circling around waiting to land) pattern (compute exact number)? a. 1 b. 1.33 c. 2 d. 1.67

Option b that is 1.33 is the right choice.

Step-by-step explanation:

Given:

Mean rate of arrival = 8 planes/hr

Service time = minute/plane

Mean service rate   = = planes/hr

Applying the concept Poisson-distributed arrival and service rates (exponential inter-arrival and service times)(M/M/1) process:

We have to find mean number of planes waiting to land that is mean number of customers in the queue .

Mean number of customers in queue .

⇒

   Considering, , is also mean number of customers in service.

⇒

⇒ Plugging the values.

⇒

⇒

⇒

So,

Mean number of planes in holding and waiting to land = 1.33

b 1: 45 am

step-by-step explanation:

its that because if it was in the pm it would be 1345

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be