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Anika [276]
2 years ago
3

Telephone calls arrive at the Global Airline reservation office in Louisville according to a Poisson distribution with a mean of

1.2 calls per minute.
a. What is the probability of receiving exactly one call during a one-minute interval?



b. What is the probability of receiving at most 2 calls during a one-minute interval?



c. What is the probability of receiving at least two calls during a one-minute interval?



d. What is the probability of receiving exactly 4 calls during a five-minute interval?



e. What is the probability that at most 2 minutes elapse between one call and the next?
Mathematics
1 answer:
otez555 [7]2 years ago
3 0

Answer:

a) 0.3614

b) 0.8795

c) 0.3374

d) 0.1338

e) 0.9093

Step-by-step explanation:

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Suppose that for a recent admissions class, an Ivy League college received 2,851 applications for early admission. Of this group
stepan [7]

Answer:

A) The probability is a measure of the likelihood than an event is going to occur. In this case we can calculate the probability of X as:

P(X) = X/N where X is the number of ways X occurs and N is the total number of events.

P(E) = E/N = 1033/2851 = 0.3623

P(R) = R/N = 854/2851 = 0.2995

P(D) = D/N = 964/2851 = 0.3381

B)

E and D are mutually exclusive because the students that were admitted early where not deffered to regular admission pool. There is no chance that there is a student that were admitted erarly and deffered at the same time, so the intersection between E and D (E∩D) is 0.

C) The number of students that were early accepted is 1033 and the total number of students accepted is 2375. The probability is going to be:

P = 1033/2375 = 0.4349

D)

In this case we can reformulate the question as: What is the probability of being accepted if you apply for early admission? This

Since 18% of the students deffered to regular admission pool 0.18 × 964 = 174 were admitted at the end.

The probability of being deffered and then accepted is going to be:

P(DA) = 174/2831 = 0.0610

The probability of ramdomly selecting a students that has been early accepted or deffered and then accepted is going to be:

P(E or DA) = 0.0610 + 0.3623 = 0.4233

This is the addition rule.

3 0
2 years ago
On one afternoon in a shoe warehouse, three large shipments of shoes arrived. The weights of the shipments were 1 ton 115 pounds
Goryan [66]

Alright, lets get started.

The weight of first shipment = 1 ton 115 pounds

As we know, 1 ton = 2000 pounds, so

So, the weight of first shipment = 2000 + 115 = 2115 pounds

The weight of second shipment = 1723 pounds 7 ounces

The weight of third shipment = 957 pounds 11 ounces

So, adding all three weights = 2115 pounds + 1723 pounds 7 ounces + 957 pounds 11 ounces

So, all three weights = 4795 pounds 18 ounces

As we know, 16 ounces = 1 pound, so

all three weights = 4795 pound 1 pound 2 ounces

All three weights = 4796 pounds 2 ounces

4796 could be wriiten as 4000 + 796

As we know, 2000 pound = 1 ton so

All three weight = 2 tons 796 pounds 2 ounces

So, the total weight of three shipments = 2 tons 796 pounds 2 ounces   :   Answer

8 0
2 years ago
Vanessa draws one side of an equilateral triangle ABC on the coordinate plane at points A(-2, 1) and B (4, 1). What are the two
Readme [11.4K]

Answer:

two vertex are: (1 , 6.2) , (1 , - 4.2)

Step-by-step explanation:

A(-2, 1) and B (4, 1)    AB is a parallel segment with  x axis

The 3rd vertex P (x , y) will locate at the mid point of AB

x = (-2) + (4 - (-2)) /2 = 1       P (1 , y)

length AB = 4 - (-2) = 6

AP = AB (equilateral)

BP² = (4 - 1)² + (1 - y)² = 6²

1 - 2y + y² = 36 - 9 = 27

y² - 2y -26 = 0

y = ((-(-2)) ± √(-2)² - 4 x (-26)) / 2 = (2 ± √108) / 2 = 1 ± 5.2

y = 6.2 or y = -4.2

P (1 , 6.2) or P ( 1 , -4.2)

5 0
2 years ago
For a certain type of copper wire, it is knownthat, on the average, 1.5 flaws occur per millimeter.Assuming that the number of f
mario62 [17]

Answer:

The probability that no flaws occur in a certain portion of wire of length 5 millimeters =  1.1156 occur / millimeters

Step-by-step explanation:

<u>Step 1</u>:-

Given data A copper wire, it is known that, on the average, 1.5 flaws occur per millimeter.

by  Poisson random variable given that λ = 1.5 flaws/millimeter

Poisson distribution P(X= r) = \frac{e^{-\alpha } \alpha ^{r} }{r!}

<u>Step 2:</u>-

The probability that no flaws occur in a certain portion of wire

P(X= 0) = \frac{e^{-1.5 } \(1.5) ^{0} }{0!}

On simplification we get

P(x=0) = 0.223 flaws occur / millimeters

<u>Conclusion</u>:-

The probability that no flaws occur in a certain portion of wire of length 5 millimeters = 5 X P(X=0) = 5X 0.223 = 1.1156 occur / millimeters

5 0
2 years ago
A storage tank is a right-circular cylinder 20 ft long and 8 ft in diameter with its axis horizontal. If 3 the tank is half full
Arada [10]

Answer:

Step-by-step explanation:

The step by step calculation is as shown in the attached file.

3 0
2 years ago
Read 2 more answers
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