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Tems11 [23]
3 years ago
9

Emergency 911 calls to a small municipality in Idaho come in at the rate of one every two minutes. Assume that the number of 911

calls is a random variable that can be described by the Poisson distribution.
(a) What is the expected number of 911 calls in one hour? per hour
(b) What is the probability of three 911 calls in five minutes? If required, round your answer to four decimal places.
(c) What is the probability of no 911 calls during a five-minute period? If required, round your answer to four decimal places.
Mathematics
1 answer:
nordsb [41]3 years ago
4 0

Answer: a) 30, b) 0.2138, c) 0.0820

Step-by-step explanation:

Since we have given that

X be the number of calls in 1 hour = 60 minutes

Rate of one call every two minutes.

\lambda=\dfrac{1}{2}

(a) What is the expected number of 911 calls in one hour?

\lambda=\dfrac{1}{2}\times 60=30

(b) What is the probability of three 911 calls in five minutes? If required, round your answer to four decimal places.

\lambda=\dfrac{1}{2}\times 5=2.5

Number of calls = 3

So, P(X=3) is given by

P(X=3)=\dfrac{e^{-\lambda}\lambda^x}{x!}\\\\P(X=3)=\dfrac{e^{-2.5}\times (2.5)^3}{3!}\\\\P(X=3)=0.2138

(c) What is the probability of no 911 calls during a five-minute period? If required, round your answer to four decimal places.

P(X=0)=\dfrac{e^{-2.5}(2.5)^0}{0!}=0.0820

Hence, a) 30, b) 0.2138, c) 0.0820

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tino4ka555 [31]

Answer:

231

Step-by-step explanation:

Given

\frac{4}{77}=\frac{12}{x}

Cross Multiply

x \times 4=12\times 77\\x=\frac{12\times 77}{4} \\x= 3\times 77\\x= 231

Therefore x=231

7 0
3 years ago
Miss has a sheet of wrapping paper 85cm in length and 60 cm in width. She cuts the paper into rectangular pieces of length 20 cm
dalvyx [7]

Answer:

Part a - 25 pieces

Part b - 4 sheets

Step-by-step explanation:

<u>Part a</u>

Think of this in terms of how many "units" can the total paper be cut into. Easiest way to keep track of units is by their area. In other words, take the total area and see how many unit areas fit into it:

Number of units = total area / unit area

N = (85 x 60) / (20 x 10)

N = 5100 / 200

N = 25.5

Therefore the greatest number of pieces the paper can be cut into is 25 units (the 0.5 doesn't count since it's not a full pieces).

<u>Part b</u>

Again, back to units. This time the "total" is 100, and our unit size is 25.5. So:

Number of units = total gifts / gifts per unit

N = 100 / 25.5

N = 3.9

Therefore 4 sheets of wrapping paper will be needed (you need to round the 3.9 up because wrapping paper sheets only come in whole numbers for the purposes of this question).

7 0
3 years ago
I need help with this question! Will mark brainliest :)
Dvinal [7]

Answer:

y=3x-2

Step-by-step explanation:

you find the 3 (the slope) by seeing how much the y value grows

the -2 is the value of the y-intercept (more clear on a graph) but it's when the point is (0,__) so you subtract 3 from 1.

3 0
3 years ago
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Can someone help me work through this ??
S_A_V [24]
The interpretation of the solution is that there are 15 true/false questions and 5 multiple choice questions.
3 0
3 years ago
Please answer number 3
Elan Coil [88]

Answer:

1250

Step-by-step explanation:

?/5000 = 25/100 5,000x25= 125,000 divided by 100= 1250.00= 1250

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3 years ago
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