Sandy charges each family that she babysits for a flat fee of $10 for the night and $5 extra per

Mid-West Publishing Company publishes college textbooks. The company operates an 800 telephone number whereby potential adopters

s344n2d4d5 [400]

The various answers to the question are:

To answer 90% of calls instantly, the organization needs four extension lines.
The average number of extension lines that will be busy is Four
For the existing phone system with two extension lines, 34.25 % of calls get a busy signal.

<h3>How many extension lines should be used if the company wants to handle 90% of the calls immediately?</h3>

a)

A number of extension lines needed to accommodate $90 in calls immediately:

Use the calculation for busy k servers.

$P_{j}=\frac{\frac{\left(\frac{\lambda}{\mu}\right)^{j}}{j !}}{\sum_{i=0}^{k} \frac{\left(\frac{\lambda}{\mu}\right)^{t}}{i !}}$

The probability that 2 servers are busy:

The likelihood that 2 servers will be busy may be calculated using the formula below.

$P_{2}=\frac{\frac{\left(\frac{20}{12}\right)^{2}}{2 !}}{\sum_{i=0}^{2} \frac{\left(\frac{20}{12}\right)^{t}}{i !}}$$\approx 0.3425$$

Hence, two lines are insufficient.

The probability that 3 servers are busy:

Assuming 3 lines, the likelihood that 3 servers are busy may be calculated using the formula below.

$P_{j}=\frac{\frac{\left(\frac{\lambda}{\mu}\right)^{j}}{j !}}{\sum_{i=0}^{2} \frac{\left(\frac{\lambda}{\mu}\right)^{i}}{i !}}$ \\\\$P_{3}=\frac{\frac{\left(\frac{20}{12}\right)^{3}}{3 !}}{\sum_{i=0}^{3} \frac{\left(\frac{20}{12}\right)^{1}}{i !}}$$\approx 0.1598$$

Thus, three lines are insufficient.

The probability that 4 servers are busy:

Assuming 4 lines, the likelihood that 4 of 4 servers are busy may be calculated using the formula below.

$P_{j}=\frac{\frac{\left(\frac{\lambda}{\mu}\right)^{j}}{j !}}{\sum_{i=0}^{k} \frac{\left(\frac{\lambda}{\mu}\right)^{t}}{i !}}$ \\\\$P_{4}=\frac{\frac{\left(\frac{20}{12}\right)^{4}}{4 !}}{\sum_{i=0}^{4} \frac{\left(\frac{20}{12}\right)^{7}}{i !}}$$

Generally, the equation for is mathematically given as

To answer 90% of calls instantly, the organization needs four extension lines.

b)

The probability that a call will receive a busy signal if four extensions lines are used is,

$P_{4}=\frac{\left(\frac{20}{12}\right)^{4}}{\sum_{i=0}^{4} \frac{\left(\frac{20}{12}\right)^{1}}{i !}} $\approx 0.0624$$

Therefore, the average number of extension lines that will be busy is Four

c)

In conclusion, the Percentage of busy calls for a phone system with two extensions:

The likelihood that 2 servers will be busy may be calculated using the formula below.

$P_{j}=\frac{\left(\frac{\lambda}{\mu}\right)^{j}}{j !}$$\\\\$P_{2}=\frac{\left(\frac{20}{12}\right)^{2}}{\sum_{i=0}^{2 !} \frac{\left(\frac{20}{12}\right)^{t}}{i !}}$$\approx 0.3425$$

For the existing phone system with two extension lines, 34.25 % of calls get a busy signal.

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3 0

1 year ago

What is the answer to this problem?

Andrei [34K]

i think the best answer for this question is A)

5 0

3 years ago

What two numbers have an absolute value of 16

Harrizon [31]

Both the negative and positive counterparts of a number have the same absolute value, or distance from 0.

The two numbers are 16 and -16.
They both have the same absolute value, 16.

7 0

2 years ago

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Suppose 72 gallons of water came out of a pipe in 8 minutes.

Masteriza [31]

Answer:

9 gallons of water per minute

Step-by-step explanation:

First identify what you know:

1) The pipe was flowing water for eight minutes.

2) In that eight minutes, 72 gallons of water came out.

So, if 72 gallons of water came out in eight minutes, how many gallons flowed out in a single minute? Well, assuming that the flow rate was consistent, then simply divide the total number of gallons that flowed out, by the number of minutes the pipe was open!

72/8 = 9

The pipe released 9 gallons of water per minute, thus resulting in 72 gallons of water in 8 minutes!

Hope this helps! :)

4 0

2 years ago

Which is true about the polynomial –8m3 + 11m?

Mumz [18]

Answer:

b) It is a binomial with a degree of 3.

Step-by-step explanation:

We need to find about which is true about the polynomial –8m3 + 11m from the given choices.

There are two terms so it is binomial.

Highest exponent on variable m is 3 so degree is 3.

Correct matching choice is "It is a binomial with a degree of 3."

Hence final answer is choice "b) It is a binomial with a degree of 3."

4 0

2 years ago

Read 2 more answers