1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Travka [436]
3 years ago
7

1Y, the number of accidents per year at a given intersection, is assumed to have a Poisson distribution. Over the past few years

, an average of 36 accidents per year have occurred at this intersection. If the number of accidents per year is at least 45, an intersection can qualify to be redesigned under an emergency program set up by the state. Approximate the probability that the intersection in question will come under the emergency program at the end of the next year.I'm thinking of using the Central Limit Theorem but I'm not exactly sure what that'll look like and the parameters used.
Mathematics
1 answer:
miss Akunina [59]3 years ago
7 0

Answer:

The probability that the intersection will come under the emergency program is 0.1587.

Step-by-step explanation:

Lets divide the problem in months rather than in years, because it is more suitable to divide the period to make a better approximation. If there were 36 accidents in average per year, then there should be 3 accidents per month in average. We can give for the amount of accidents each month a Possion distribution with mean 3 and variance 3.

Since we want to observe what happen in a period of one year, we will use a sample of 12 months and we will take its mean. We need, in average, more than 45/12 = 3.75 accidents per month to confirm that the intersection will come under the emergency program.

For the central Limit theorem, the sample mean will have a distribution Normal with mean 3 and variance 3/12 = 0.25; thus its standard deviation is √0.25 = 1/2.

Lets call the sample mean distribution X. We can standarize X obtaining a standard Normal random variable W with distribution N(0,1).

W = \frac{X-\mu}{\sigma} = \frac{X-3}{1/2} = 2x-6

The values of \phi , the cummulative distribution function of W, can be found in the attached file. We are now ready to compute the probability of X being greater than 3.75, or equivalently, the probability than in a given year the amount of accidents is greater than 45, leading the intersection into an emergency program

P(X > 3.75) = P(2X-6 > 2*3.75-6) = P(W > 1) = 1-\phi(1) = 1-0.8413 \\= 0.1587

Download pdf
You might be interested in
It takes 8 cups of chicken broth to make a chicken soup recipe. How much is this in quarts?
irakobra [83]
There are 4 cups per 1 quart...

4/1 × 2/2 = 8/2

There are 8 cups in 2 quarts.
7 0
3 years ago
Find the equation of the sphere passing through P(negative 4 comma 7 comma 6 )and Q(8 comma negative 3 comma 5 )with its center
Juli2301 [7.4K]

Answer: The equation of the sphere is:

(x-2)^2 + (y-2)^2 + (z-5/2)^2 = sqrt(245)/2

Step-by-step explanation:

The centre of the sphere is the midpoint of the diameter, which is

1/2

[(-4,7,6) + (8,-3,5)] =(2,2,5/2)

The length of the diameter is

=sqrt |(8,-3,5) - (-4,7,6)|^2

=sqrt (12^2 + (-10)^2 + (-1)^2)

=sqrt (144+100+1)

=sqrt(245)

so the radius of

the sphere is:

1/2(sqrt(245)) = sqrt(245)/2.

The equation of the sphere is:

(x-2)^2 + (y-2)^2 + (z-5/2)^2 = sqrt(245)/2

4 0
3 years ago
What is the surface area of this shape?<br> 1 cm<br> 5 cm<br> 4 cm<br> 2 cm<br> 6 cm<br> 3 cm
a_sh-v [17]

Answer:

88 cm²

Step-by-step explanation:

Each square is 1 cm². Count the squares of each face and add them.

Front face (purple): 14 cm²

Back face (hidden): 14 cm²

Right lower face (orange): 6 cm²

Right upper face (orange): 6 cm²

Left face (hidden): 12 cm²

Upper top face (blue): 3 cm²

Lower top face (blue): 15 cm²

Bottom face (hidden): 18 cm²

Add all areas above:

88 cm²

7 0
2 years ago
Mrs. Taylor made 67 tissue holders each day. She decided to sell her tissue holders and sold out each day for four weeks. How ma
poizon [28]

Answer:

the answer would be A

Step-by-step explanation:

3 0
3 years ago
Landscape company sold 25 trees on Friday. There were a total of 125 trees in inventory. What percent of the trees were sold on
Arte-miy333 [17]

Answer: 20%

Step-by-step explanation:

First determine how many times 25 fits in 125. It’s 5 right. Now turn that into a percent. That leading to 20%

5 0
3 years ago
Read 2 more answers
Other questions:
  • Convert 22 meters to millimeters​
    7·1 answer
  • If f(x) = square root of x+3, what is the equation for f–1(x)? f–1(x) = x2 - 3 f–1(x) = x2 + 3 f–1(x) = (x - 3) 2 f–1(x) = (x +
    8·1 answer
  • What does coeffient stand for
    10·2 answers
  • Suppose that X is the number of hours that a computer is used in a computer lab on campus. The table below is the probability di
    11·1 answer
  • Trying to get down with summer school today and I’ve done most of it but a few.
    15·1 answer
  • Design specifications require that a key dimension on a product measure 100 /- 10 units. A process being considered for producin
    15·1 answer
  • Assume y=5x and dx/dt = 2 find dy/dt
    9·1 answer
  • Yousuf buys a pen that cost AED 2.12. How much will 4 such pen cost? GUYS PLEASE QUICK I HAVE AN EXAM RN
    6·2 answers
  • David has a stack of 30 cards, which are numbered 1 through 30. what is the exact probability of randomly selecting a card from
    6·1 answer
  • Rewrite the equation in Ax+By=C form.<br> Use integers for A, B, and C.<br> y+1=2(x+5)
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!