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
Arte-miy333 [17]
3 years ago
13

The number of flaws in a fiber optic cable follows a Poisson distribution. It is known that the mean number of flaws in 50m of c

able is 1.2. a) What is the probability of exactly three flaws in 150m of cable? b) What is the probability of at least two flaws in 100m of cable? c) What is the probability of exactly one flaw in the first 50m of cable, and exactly one flaw in the second 50m of cable?
Mathematics
1 answer:
boyakko [2]3 years ago
4 0

Answer:

(a) The probability of exactly three flaws in 150 m of cable is 0.21246

(b) The probability of at least two flaws in 100m of cable is 0.69155

(c) The probability of exactly one flaw in the first 50 m of cable, and exactly one flaw in the second 50 m of cable is 0.13063

Step-by-step explanation:

A random variable X has a Poisson distribution and it is referred to as Poisson random variable if and only if its probability distribution is given by

p(x;\lambda)=\frac{\lambda e^{-\lambda}}{x!} for x = 0, 1, 2, ...

where \lambda, the mean number of successes.

(a) To find the probability of exactly three flaws in 150 m of cable, we first need to find the mean number of flaws in 150 m, we know that the mean number of flaws in 50 m of cable is 1.2, so the mean number of flaws in 150 m of cable is 1.2 \cdot 3 =3.6

The probability of exactly three flaws in 150 m of cable is

P(X=3)=p(3;3.6)=\frac{3.6^3e^{-3.6}}{3!} \approx 0.21246

(b) The probability of at least two flaws in 100m of cable is,

we know that the mean number of flaws in 50 m of cable is 1.2, so the mean number of flaws in 100 m of cable is 1.2 \cdot 2 =2.4

P(X\geq 2)=1-P(X

P(X\geq 2)=1-p(0;2.4)-p(1;2.4)\\\\P(X\geq 2)=1-\frac{2.4^0e^{-2.4}}{0!}-\frac{2.4^1e^{-2.4}}{1!}\\\\P(X\geq 2)\approx 0.69155

(c) The probability of exactly one flaw in the first 50 m of cable, and exactly one flaw in the second 50 m of cable is

P(X=1)=p(1;1.2)=\frac{1.2^1e^{-1.2}}{1!}\\P(X=1)\approx 0.36143

The occurrence of flaws in the first and second 50 m of cable are independent events. Therefore the probability of exactly one flaw in the first 50 m and exactly one flaw in the second 50 m is

(0.36143)(0.36143) = 0.13063

You might be interested in
3. Given AB with coordinates A(-4,5) and B(12,13). Find the horizontal distance and the vertical
SCORPION-xisa [38]

The required distance would be 17.88 units coordinates A(-4,5) and B(12,13) and the horizontal distance is 16 units and the vertical distance is 8 units from A to B which are determined by the graphing method.

<h3>What is the distance between two points?</h3>

The distance between two points is defined as the length of the line segment between two places representing their distance.

Given AB with coordinates A(-4,5) and B(12,13).

The formula of the distance between two points is A(x₁, y₁) and B(x₂, y₂) is given by: d (A, B) = √ (x₂ – x₁)² + (y₂ – y₁) ².

x₁ = -4, y₁ = 5

x₂ = 12, y₂ = 13

distance = √ (12 – (-4))² + (13 – 5)²

distance = √ (12 + 4)² + (8)²

distance = √ (16)² + (8)²

distance = √ (256 + 64)

distance = √320

distance = 17.88 units

The horizontal distance is 16 units and the vertical distance is 8 units from A to B which are determined by the graphing method.

Learn more about the distance between two points here:

brainly.com/question/15958176

#SPJ1

6 0
1 year ago
Laura determined the difference between 8 and –2 using the additive inverse. Her steps are shown below.
NNADVOKAT [17]

Answer: The 8 should have remained positive.

6 0
2 years ago
Read 2 more answers
What is that simplest form of 9*5/6?​
Arturiano [62]

Answer:

7 1/2

Before simplification: 15/2

Step-by-step explanation:

6 0
3 years ago
A garage contains a combination of 20 bicycles and tricycles in total,there are 44 wheels how many bicycles and how many tricycl
Amanda [17]

4 tricycles and 16 bicycles

hope this helps

4 0
3 years ago
PLEASE HELP (AGAIN) LOOK AT PIC
Serhud [2]

Answer: it should be 60

Step-by-step explanation:

6 0
3 years ago
Other questions:
  • WILL GIVE A BRAINLIEST!!
    6·1 answer
  • Why is it important to choose a bank that is a member of the FDIC?
    15·2 answers
  • CW
    10·1 answer
  • Doctor Jon sees 6 patients in 1 1⁄2 hours. Doctor Carol sees 10 patients in 2 hours. Which doctor sees more patients per hour?
    6·1 answer
  • A class is divided into 4 groups. A bag contains pieces of paper that are red, blue, green, and yellow. For every blue- or green
    13·1 answer
  • Sally's cat is 3 years older than Helen's dog. The product of their ages is 54. How old is Helen's dog?
    10·1 answer
  • Please help its due today
    11·1 answer
  • WILL GIVE BRAINLIEST. It is also worth 34 POINTS!!! PLEASE HELP!!!! Please respond in full sentences. I appreciate your help. Th
    12·1 answer
  • Solve the simultaneous equations<br> 2x+3y20 <br> 2x+5=10
    15·1 answer
  • Can soeone answer this asap pleasee?
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!