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
Nataly_w [17]
3 years ago
7

At a specific point on a highway, vehicles arrive according to a Poisson process. Vehicles are counted in 12 second intervals, a

nd vehicle counts are taken in 120 of these time intervals. No cars arrive in 15 of these 120 intervals. a. Approximate the number of these intervals in which exactly one car arrives. (1 point) b. Estimate the percentage of time headways that will be 14 seconds or greater. (1 point) Hint: use t=14 seconds and x=0
Mathematics
1 answer:
morpeh [17]3 years ago
7 0

Answer: a) 4.6798, and b) 19.8%.

Step-by-step explanation:

Since we have given that

P(n) = \dfrac{15}{120}=0.125

As we know the poisson process, we get that

P(n)=\dfrac{(\lambda t)^n\times e^{-\lambda t}}{n!}\\\\P(n=0)=0.125=\dfrac{(\lambda \times 14)^0\times e^{-14\lambda}}{0!}\\\\0.125=e^{-14\lambda}\\\\\ln 0.125=-14\lambda\\\\-2.079=-14\lambda\\\\\lambda=\dfrac{2.079}{14}\\\\0.1485=\lambda

So, for exactly one car would be

P(n=1) is given by

=\dfrac{(0.1485\times 14)^1\times e^{-0.1485\times 14}}{1!}\\\\=0.2599

Hence, our required probability is 0.2599.

a. Approximate the number of these intervals in which exactly one car arrives

Number of these intervals in which exactly one car arrives is given by

0.2599\times 18=4.6798

We will find the traffic flow q such that

P(0)=e^{\frac{-qt}{3600}}\\\\0.125=e^{\frac{-18q}{3600}}\\\\0.125=e^{-0.005q}\\\\\ln 0.125=-0.005q\\\\-2.079=-0.005q\\\\q=\dfrac{-2.079}{-0.005}=415.88\ veh/hr

b. Estimate the percentage of time headways that will be 14 seconds or greater.

so, it becomes,

P(h\geq 14)=e^{\frac{-qt}{3600}}\\\\P(h\geq 14)=e^{\frac{-415.88\times 14}{3600}}\\\\P(h\geq 14)=0.198\\\\P(h\geq 14)=19.8\%

Hence, a) 4.6798, and b) 19.8%.

You might be interested in
Say that every single class in Full Sails Masters Degree in Game Design has a 5% failure rate
natka813 [3]
The monthly failure rate is q = 5% = 0.05
The monthly pass rate is p = 1 - q = 0.95

We want to determine the probability of 12 passes in 12 consecutive months for a student.
P(12 of 12 successes) = ₁₂C₁₂ p¹² q⁰ = 0.95¹² = 0.5404.

Therefore if we have 100 students, the number that gets through 12  consecutive months is
100*005404 = 54 students.

Answer: 54 students are left after 12 months.
6 0
3 years ago
21x+7y=42 and -5x+5y=10 <br>Find the solution to the system of equations​
stiv31 [10]

Answer:

Step-by-step explanation:

x=1 y=3

5 0
3 years ago
What is the solution to the equation 3(2x+5)=3x+4x<br> A.x=0<br> B.x=4<br> C.x=5<br> D.x=15
Ivan

x=15 and i have to write some more for 20 letters

6 0
3 years ago
Read 2 more answers
Daniel and Alice each earn money by babysitting. Daniel earned a total of $84 in a 5-week period. During a 6-week period, Alice
sweet [91]

Answer:12

Step-by-step explanation:

16 • 6= 96

96-84=12

4 0
3 years ago
What is the solution of each system of equations? Show your work-6x-5y=64x+y=3
elena55 [62]

Answer:

-6y = 70x = 3

Step-by-step explanation:

-6x - 5y= 64x+ y=3

 ---------------------------  

       -y            - y

---------------------------------

-6x -6y = 64x = 3

------------------------------------

+6x        +6x

-------------------------------------

-6y = 70x = 3

6 0
3 years ago
Read 2 more answers
Other questions:
  • What is the value of x? show all of your work!​
    15·1 answer
  • Please help! 10+ Mpoints
    7·1 answer
  • 5+5 is what plz help<br>​
    9·2 answers
  • A cone is 6 cm in height and its vertical angle is 54° calculate the radius of its base.
    7·1 answer
  • How do you find the value of 35(10^-8)? Find the answer.
    15·1 answer
  • What is the distance between (2, 5) and (2, -7)?
    15·1 answer
  • MARKING BRAINLIEST PLZ HELP! You are given the following five lines:
    6·1 answer
  • Help! Help! Help! Help! Help! Help! ​
    12·1 answer
  • Need help ASAP! Please
    6·2 answers
  • Evaluate f(x) = -x power of 2 -4 for x=-3
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!