In a waiting line system, there is only one server. Customer arrivals follow Poisson distribution with mean inter-arrival time 5 minutes. Service time follow exponential distribution and a server can serve 15 customers per hour on average. What is the average waiting time?

Question 2 options:

a)

2 min

b)

none of the answer

c)

20 min

d)

30 min

e)

16 min

in a waiting line system, there is only one server. Customer arrivals follow Poisson distribution with mean inter-arrival time 5 minutes. Service time follow exponential distribution and a server can serve 15 customers per hour on average. What is the average waiting time? Question 2 options: a) 2 min b) none of the answer c) 20 min d) 30 min e) 16 min

The answer is d

Explanation:

Arrival rate = 5 minutes

Service rate = 15 customer per hour

ts = Arrival rate / service rate - Arrival rate

= 5/ 15 - 5

= 5/ 10

= 0.5

Since 60 minutes = 1 hour

= 0.5 × 60

= 30 minutes

bd = 9 cm

step-by-step explanation:

in a 30°-60°-90° triangle, the ratio of side lengths is 1 : √3 : 2. that is, the longest side (hypotenuse) is twice the length of the shortest side.

all of the triangles in your geometry are 30°-60°-90° triangles. ac is the hypotenuse of δacd, and the short side of δabc.

the short side ad of δacd will be half the length of ac, so 3 cm. the hypotenuse ab of δabc will be twice the length of ac, so 12 cm. segment bd is the difference of the lengths ab and ad, so is

bd = ab -ad

bd = 12 cm - 3 cm = 9 cm

comment on side length ratios

you can figure the ratios of side lengths in a 30°-60°-90° triangle by considering the trig ratios of the angles. or you can figure the length of the altitude of an equilateral triangle of side length 2 using the pythagorean theorem.

answer; conceptual skills;