answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Nonamiya [84]
2 years ago
12

Customers enter the waiting line at a cafeteria on a first-come, first-served basis. The arrival rate follows a Poisson distribu

tion, while service times follow an exponential distribution. If the average number of arrivals is four per minute and the average service rate of a single server is seven per minute, what is the average number of customers waiting in line behind the person being served
Mathematics
1 answer:
Veseljchak [2.6K]2 years ago
3 0

Answer:

The average number of customers waiting in line behind the person being served is 0.7619.

Step-by-step explanation:

In queueing problem, an M/M/1 queue model is an arrangement with a single queue, where arrivals at the queue are approximated by a Poisson distribution with mean <em>λ</em> and the service times follows an exponential distribution with mean <em>μ</em>.  

The mean number of arrivals in this system is given by:

\text{Average number of customers}=\frac{\rho}{1-\rho}

Here the variable <em>ρ</em> is defined as:

\rho=\frac{\lambda}{\mu}

From the average number of arrivals in the system, we can calculate the average number of  arrivals in the queue by subtracting the average number of arrivals in service.

That is,

\text{Average number of customers in the queue}=\frac{\rho}{1-\rho}-\rho =\frac{\rho^{2}}{1-\rho}

The information provided is:

The average number of arrivals of customers is, <em>λ</em> = 4.

The average service rate of a single server is, <em>μ</em> = 7.

Compute the average number of customers waiting in line behind the person being served as follows:

\text{Average number of customers in the queue}=\frac{\rho}{1-\rho}-\rho =\frac{\rho^{2}}{1-\rho}

                                                                   =\frac{(4/7)^{2}}{1-(4/7)}\\\\=\frac{(4/7)^{2}}{(7-4)/7}\\\\ =\frac{16}{49}\times \frac{7}{3}\\\\=0.7619

Thus, the average number of customers waiting in line behind the person being served is 0.7619.

You might be interested in
Sean tried to drink a slushy as fast as he could. He drank the slushy at a constant rate. There were originally 275 milliliters
Inga [223]

Answer:

Step-by-step explanation:

275 (slushy) in a cup.

After 13 seconds, 210 milliliters of slushy remained.

divide the original by the seconds then the answer by the left over. And then you get your answer.

hope it helps!

please give me brainliest  

5 0
2 years ago
Read 2 more answers
Consider a data set with at least three data values. Suppose the highest value is increased by 10 and the lowest is decreased by
bulgar [2K]

Answer:

a. Mean doesn't change.

b. Median doesn't change.

c. Mode can change.

Step-by-step explanation:

Let us assume the data set with 10 observations

{2,6,4,3,2,6,4,9,4,7}.

Arranging data set in ascending order

{2,2,3,4,4,4,6,6,7,9}

mean=2+2+3+4+4+4+6+6+7+9/10=4.7

median

n/2=10/2=5 is an integer so,

median= average of n/2 and n/2 +1

median= (5th value+6th value)/2

median=(4+4)/2=8/2=4

Mode

The most repeated value is 4. So, mode is 4 for assumed data.

Increasing highest value by 10 and decreasing lowest value by 10

{-8,2,3,4,4,4,6,6,7,19}

a.

mean=-8+2+3+4+4+4+6+6+7+19/10=4.7

Mean doesn't change

b.

median

n/2=10/2=5 is an integer so,

median= average of n/2 and n/2 +1

median= (5th value+6th value)/2

median=(4+4)/2=8/2=4

Median doesn't change

c.

Most occurring value is still 4. But mode can change if the value the highest value becomes most concurring value.

5 0
2 years ago
Read 2 more answers
If mc020-1.jpg and mc020-2.jpg, what is the domain of mc020-3.jpg?
ludmilkaskok [199]

we have

f(x)=x+7

g(x)=\frac{1}{x-13}

(fog)(x)=[\frac{1}{x-13}]+7

we know that

the denominator cannot be zero, therefore the value of x cannot be 13

The domain are all real numbers except the number 13

therefore

<u>the answer is the option</u>

{x|≠13}



3 0
2 years ago
Read 2 more answers
An animal shelter needs to find homes for 40 dogs and 60 cats. If 15% of the dogs are female, and 25% of the cats are female, wh
Harrizon [31]

Answer:

21% of the animals are female

Step-by-step explanation:

In total:

There are 40 + 60 = 100 animals.

Female animals.

40 dogs. Of those, 15% are female. So 0.15*40 = 6.

60 cats. Of those, 25% are female. So 0.25*60 = 15.

21 female animals.

21/100 = 0.21 = 21%

21% of the animals are female

3 0
2 years ago
A disadvantage of the contention approach for LANs, such as CSMA/CD, is the capacity wasted due to multiple stations attempting
sammy [17]

Answer:

The overview of the given problem is outlined in the following segment on the explanation.

Step-by-step explanation:

The proportion of slots or positions that have been missed due to numerous concurrent transmission incidents can be estimated as follows:

Checking a probability of transmitting becomes "p".

After considering two or even more attempts, we get

Slot fraction wasted,

= [1-no \ attempt \ probability-first \ attempt \ probability-second \ attempt \ probability+...]

On putting the values, we get

= 1-no \ attempt \ probability-[N\times P\times probability \ of \ attempts]

= 1-(1-P)^{N}-N[P(1-P)^{N}]

So that the above seems to be the right answer.

8 0
2 years ago
Other questions:
  • Jillian is selling boxes of cookies to raise money for her basketball team. the 10 oz. box costs $3.50, while the 16 oz. box cos
    12·2 answers
  • What is one of the zeros of the function shown in this graph?
    14·2 answers
  • A home improvement store advertises 60 square feet of flooring for $287.00 including an $80.00 installation fee. Write an equati
    8·1 answer
  • Find the sum of the first 63 terms of –19, -13, -7 …
    10·1 answer
  • As part of a company incentive, each sales person that sells over \$40{,}000$40,000dollar sign, 40, comma, 000 in merchandise th
    5·2 answers
  • Dan invests £1200 into his bank account.
    8·2 answers
  • red and blue ceramic tiles are laid according to a pattern such that every 21 red tiles used, 4 blue tiles are used. if a total
    11·1 answer
  • Tom and jerry have to stuff and seal 63 envelopes for a new marketing campaign. Jerry can stuff and seal 15 envelopes alone in 2
    6·1 answer
  • Is ½y=1 a linear equation ​
    6·1 answer
  • Is it possible to form a triangle with side lengths 3.5 3.5, and 9? If so, will it be scalene, isosceles, or equilateral? Or non
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!