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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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What are both of these shaded as?
Sedaia [141]

Answer:

1 whole and 15/100= <em><u>1.15</u></em>

Step-by-step explanation:

The first box is 1 whole, in total there are 100 squares. All u need to do is count the number of squares

4 0
3 years ago
Patrick wanted to gather data about the cost of joining a community pool in his area. He plotted the data and determined that th
ohaa [14]

Answer:

The y-intercept is 40. This is the cost of registration ⇒ last answer

Step-by-step explanation:

* Lets explain how to solve the problem

- Patrick wanted to gather data about the cost of joining a community

 pool in his area

- He plotted the data and determined that the average community

 pool membership cost consists of a one-time registration fee and

 a monthly fee

∴ The cost consists of two parts:

# Part A: one-time registration fee, it is a fixed amount not depend on

  any other condition

# Part B: monthly fee, it depends on the number of months

- He modeled that by the equation y = 15 x + 40, where

# y is the cost for the membership

# 15 is the monthly fee

# x is the number of months

# 40 is the one-time registration

- The form of the equation is y = mx + c, where c is the y-intercept

∴ The y-intercept in the equation y = 15 x + 40 is 40

∴ The y-intercept is the one-time registration fee

* The y-intercept is 40. This is the cost of registration

4 0
3 years ago
In 2007, there were more than 8.14 million cars for sale. Over the next 3 years, the number of cars decreased by 23%. Write an e
Nina [5.8K]

Answer:

c = 8.14 million×(0.9166)^t

4.83 million  

Step-by-step explanation:

Data:

  t = y - 2007

c₀ = 8.14 million

c₃  = 23 % less than c₁

Part 1. Calculate c₃

c₃ = c₀(1 - 0.23) = 0.77c₀

Part 2. Calculate r

      c₃ = c₀r^t

0.77c₀ = c₀r³

   0.77 = r³              Divided each side by c₀

         r = 0.9166     Took the cube root of each side

The explicit decay model is c = 8.14 million×(0.9166)^t

Part 3. Prediction

t = 2013 - 2007 = 6

c = c₀r^t = 8.14 million×(0.9166)⁶ = 8.14 million × 0.5929 = 4.83 million

The model predicts that there will be 4.83 million cars for sale in 2013.

7 0
2 years ago
Help me please please
tatyana61 [14]

Answer:

6.91 times 6.91 equals 47.7481

47.7481 times π equals 150.005080183

to the second digit this is

150.01

5 0
2 years ago
Read 2 more answers
PLEASE HELP QUICKLY!!! A student's parents offer him one of two options to receive scholarship money for college.
emmainna [20.7K]

Answer:

A = $47,500.00, B = $65,536.00; B, because he receives $18,036.00 more

Step-by-step explanation:

Option A Versus Option B

Option A                                                Option B

Day Amount Deposited                        Day Amount Deposited

0     $40,000.00                                    0       $1.00

1      $40,250.00                                     1        $2.00

2      $40,500.00                                    2       $4.00

...

30   $47,500                                          16      $65,536.00

Answer:

A = $47,500.00, B = $65,536.00; B, because he receives $18,036.00 more

7 0
3 years ago
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