Phone calls arrive at the rate of 48 per hour at the reservation desk for Regional Airways. (Round your answers to four decimal places.)(a) Compute the probability of receiving two calls in a 5-minute interval of time.(b) Compute the probability of receiving exactly 10 calls in 15 minutes.(c) Suppose no calls are currently on hold. If the agent takes 5 minutes to complete the current call. how many callers do you expect to be waiting by that time?

(a) To find the probability of receiving two calls in a 5-minute interval of time, we need to first convert the arrival rate to a rate per 5 minutes. There are 12 five-minute intervals in an hour, so the arrival rate per 5 minutes is:

λ = (48 calls/hour) / (12 intervals/hour) = 4 calls/5 minutes

Using the Poisson distribution with parameter λ = 4, we can calculate the probability of receiving exactly 2 calls in a 5-minute interval:

P(X = 2) = (e^(-λ) * λ^2) / 2! = (e^(-4) * 4^2) / 2! ≈ 0.1465

Therefore, the probability of receiving two calls in a 5-minute interval is approximately 0.1465.

(b) To find the probability of receiving exactly 10 calls in 15 minutes, we need to first convert the arrival rate to a rate per 15 minutes. There are 4 fifteen-minute intervals in an hour, so the arrival rate per 15 minutes is:

λ = (48 calls/hour) / (4 intervals/hour) = 12 calls/15 minutes

Using the Poisson distribution with parameter λ = 12, we can calculate the probability of receiving exactly 10 calls in a 15-minute interval:

P(X = 10) = (e^(-λ) * λ^10) / 10! = (e^(-12) * 12^10) / 10! ≈ 0.1032

Therefore, the probability of receiving exactly 10 calls in 15 minutes is approximately 0.1032.

(c) The expected number of callers waiting by the time the agent completes the current call can be found using the formula:

E(N) = λ * t

where λ is the arrival rate and t is the time the agent takes to complete the call. Since λ = 48 calls/hour and the agent takes 5 minutes to complete the call, we need to convert the arrival rate to a rate per 5 minutes:

λ = (48 calls/hour) / (60 minutes/hour) * 5 minutes = 4 calls/5 minutes

Then, we can calculate the expected number of callers waiting:

E(N) = λ * t = 4 * 5 = 20

Therefore, we expect there to be 20 callers waiting by the time the agent completes the current call.

To Know more about  probability refer here

https://brainly.com/question/31722868#

#SPJ11

A train travels at a constant rate of 75 miles per hour. How many miles will it travel in 5 hours?

PLEASE HELP AND EXPLAIN YOUR ANSWER!

A store sells three different packs of the same yogurt. Which pack is the best buy? A) 8 containers for $4.04 B) 6 containers for $3.46 c) 4 containers for $2.84

Is the relation below a function?
-3
-1
-1
3
у
0
1
2
3

simplify -8-(12)+(-2)​

please helppppp please asap

how do you find the x-intercepts if given the following polynomial in factored form?

X(x-2)^2(x+4)(x+1)​

Guys please help

which phrase has the same meaning as 12y - 2?
​

How many vehicles are at Nam's Gas Station?

Samantha is a school leader. She wants to decide whether makeup should be allowed in school or not? So she collected random samples of 200 girls regarding girl's make up preference. There are 650 girls in her school.

When 8 is subtracted from the square of a number , the result is 7 times the number find the positive solution

what is m3 + 9n when m = 4 and n = 5

A map has a scale factor of 0.25 inch : 50 miles. On the map, the distance of a river is 2.5 inches. What is the actual distance of the river?

A nurse wants to simulate the number of male and female births at the hospital where she
works using a random digit table.
Which of the following best simulates this situation?

8(333.1)I need help please

What equation below is a perpendicular line to the line y=-4x+8

655 + (6.3 x 170) + (4.7 x 58) - (4.7 x 18)

8 + 3n ≥ 38 do yall know??? solve please

How many terms are in the expression?
12a-2c+6​

Tamara finds the sum of two number cubes rolled at the same time. The chart below shows all possible sums from the 36 possible combinations when rolling two number cubes. How many times should Tamara expect the sum of the two cubes be equal to 4 if she rolls the two number cubes 216 ​times?

qual das inequações seguintes e equivalente à inequação -2x <4?
a) x<-2
b) x>-2
c) x<2
d) x>2​

i need help. what do i do and how do I solve this?

[tex] \frac{4}{5 } + \frac{3}{20} = [/tex]
​

How many turning points are there in the graph of y = x^3 - 2x^2 - 2 ?

A. 1

B. 2

C. 3

D. 4

What is the answer to this question? x−7≤−5

Find the circumference of the circle

what is 1/6x + 3/4(1/2x - 4)?​

What is the difference?
5X
X-2
x + 4
2x
9x2 + 2x + 8
2 x(x - 2)
7x²+8
2 x(x - 2)
9x2–2x+8
2 x(x-2)
7x²-8
2X(x-2)

help i have this question and i’m not sure what the answer would be

If the radius is 10 ft, what will the area of the circle be?