Please help me with this question worth 30 point’s

A new shopping mall is considering setting up an information desk manned by one employee. Based upon information obtained from s

quester [9]

Answer:

a) $P=1-\frac{\lambda}{\mu}=1-\frac{20}{30}=0.33$ and that represent the 33%

b) $p_x =\frac{\lambda}{\mu}=\frac{20}{30}=0.66$

c) $L_s =\frac{20}{30-20}=\frac{20}{10}=2 people$

d) $L_q =\frac{20^2}{30(30-20)}=1.333 people$

e) $W_s =\frac{1}{\lambda -\mu}=\frac{1}{30-20}=0.1hours$

f) $W_q =\frac{\lambda}{\mu(\mu -\lambda)}=\frac{20}{30(30-20)}=0.0667 hours$

Step-by-step explanation:

Notation

P represent the probability that the employee is idle

$p_x$ represent the probability that the employee is busy

$L_s$ represent the average number of people receiving and waiting to receive some information

$L_q$ represent the average number of people waiting in line to get some information

$W_s$ represent the average time a person seeking information spends in the system

$W_q$ represent the expected time a person spends just waiting in line to have a question answered

This an special case of Single channel model

Single Channel Queuing Model. "That division of service channels happen in regards to number of servers that are present at each of the queues that are formed. Poisson distribution determines the number of arrivals on a per unit time basis, where mean arrival rate is denoted by λ".

Part a

Find the probability that the employee is idle

The probability on this case is given by:

In order to find the mean we can do this:

$\mu = \frac{1question}{2minutes}\frac{60minutes}{1hr}=\frac{30 question}{hr}$

And in order to find the probability we can do this:

$P=1-\frac{\lambda}{\mu}=1-\frac{20}{30}=0.33$ and that represent the 33%

Part b

Find the proportion of the time that the employee is busy

This proportion is given by:

$p_x =\frac{\lambda}{\mu}=\frac{20}{30}=0.66$

Part c

Find the average number of people receiving and waiting to receive some information

In order to find this average we can use this formula:

$L_s= \frac{\lambda}{\lambda -\mu}$

And replacing we got:

$L_s =\frac{20}{30-20}=\frac{20}{10}=2 people$

Part d

Find the average number of people waiting in line to get some information.

For the number of people wiating we can us ethe following formula"

$L_q =\frac{\lambda^2}{\mu(\mu-\lambda)}$

And replacing we got this:

$L_q =\frac{20^2}{30(30-20)}=1.333 people$

Part e

Find the average time a person seeking information spends in the system

For this average we can use the following formula:

$W_s =\frac{1}{\lambda -\mu}=\frac{1}{30-20}=0.1hours$

Part f

Find the expected time a person spends just waiting in line to have a question answered (time in the queue).

For this case the waiting time to answer a question we can use this formula:

$W_q =\frac{\lambda}{\mu(\mu -\lambda)}=\frac{20}{30(30-20)}=0.0667 hours$

6 0

2 years ago

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What is the gcf of 27 and 36

mestny [16]

The answer would be 9. 9x3=27 and 9x4=36. Although 3 fits into both, 9 is the BIGGER number that also fits into both of the numbers shown in the problem.

5 0

2 years ago

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Sierra’s ice cream shop made $45 before she had to close early when the power went out. She realized she lost Two-thirds of a do

lozanna [386]

Answer:

Sierra's profit was $41.

Step-by-step explanation:

Sierra realized she lost two-third of a dollar each hour when the shop was closed.

The expression that models this situation is, ............. (1)

Now, we have to calculate Sierra's profit if the shop was closed for 6 hours.

So, putting h = 6 hours in the equation (1) we get,

dollars.

So, Sierra's profit was $41. (Answer)

Step-by-step explanation:

3 0

3 years ago

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If Steve throws the football 50 meters in 3 seconds, what is the average speed of the football? Speed = distance / time

ankoles [38]

Answer:

A

i used calculator

6 0

3 years ago

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Which of the following words correctly describe a triangle with two 45 angles?

Tom [10]

Well, first let's identify which answers are incorrect, then it will be easier to figure out which are correct.

A. Equilateral: An equilateral triangle is a triangle with 3 equal sides. Since there are 180 degrees in a triangle, an equilateral triangle would have three sides of 60 degrees, and none of 45 degrees. Answer? Incorrect.

B. Isosceles: An isosceles triangle has two sides that are equal. 45 and 45 are equal, therefore, this answer is: Correct!

C. Scalene: A scalene triangle has three unequal sides, therefore, this answer is incorrect.

D. Obtuse: An obtuse triangle has one angle that is more than 90 degrees, therefore, since 45 and 45 equal 90 already, this answer is: incorrect.

E. Right: A right triangle has one right angle (angle that equals 90 degrees) since 45 + 45 = 90, and 90 + 90 = 180, this answer is: Correct!

F. Equiangular: This last choice is practically the same as the first, therefore the answer is: incorrect.

The two correct answers are: B Isosceles, and E Right!

4 0

3 years ago

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