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
Maru [420]
3 years ago
15

Messages arrive to a computer server according to a Poisson distribution with a mean rate of 11 per hour. Determine the length o

f an interval of time (in seconds) such that the probability that no messages arrive during this interval is 0.76. Round your answers to one decimal place (e.g. 98.7).
Mathematics
1 answer:
Zarrin [17]3 years ago
6 0

Answer:

The length of the interval during which no messages arrive is 90 seconds long.

Step-by-step explanation:

Let <em>X</em> = number of messages arriving on a computer server in an hour.

The mean rate of the arrival of messages is, <em>λ</em> = 11/ hour.

The random variable <em>X</em> follows a Poisson distribution with parameter <em>λ</em> = 11.

The probability mass function of <em>X</em> is:

P(X=x)=\frac{e^{-11}11^{x}}{x!};\ x=0,1,2,3....

It is provided that in <em>t</em> hours the probability of receiving 0 messages is,

P (X = 0) = 0.76

Compute the value of <em>t</em> as follows:

P(X=0)=\frac{e^{-11\times t}(11\times t)^{0}}{0!}\\0.76=e^{-11\times t}\\\ln(0.76)=-11\times t\\t=-\frac{\ln(0.76)}{11} \\=0.025\ hours\\\approx90\ seconds

Thus, the length of the interval during which no messages arrive is 90 seconds long.

You might be interested in
Henry had beaten 12 levels in a video game. If the ratio of levels he had beaten to not
babunello [35]
12 / 6 = 2

2 x (6 + 1) = 14
8 0
2 years ago
If two opposite sides of a quadrilateral are perpendicular and congruent, then the quadrilateral is a parallelogram.
nevsk [136]
I think this is false because two opposite sides can't be perpendicular (creating a 90 degree angle) because opposite sides are parallel.
3 0
3 years ago
Given r=3 and a center of (3,5)? Find the equation of the circle in standard and general form.
alukav5142 [94]

9514 1404 393

Answer:

  • (x -3)^2 +(y -5)^2 = 9
  • x^2 +y^2 -6x -10y +25 = 0

Step-by-step explanation:

The standard form equation for a circle of radius r and center (h, k) is ...

  (x -h)^2 +(y -k)^2 = r^2

For radius 3 and center (3, 5), this is ...

  (x -3)^2 +(y -5)^2 = 9 . . . . standard form equation

Expanding this and subtracting the constant on the right gives ...

  x^2 -6x +9 +y^2 -10y +25 -9 = 0

  x^2 +y^2 -6x -10y +25 = 0 . . . . general form equation

8 0
2 years ago
-3x - 4y = 4<br> -5.2 +y = 2<br> Is (2, 10) a solution of the system?
Dmitrij [34]

Answer:

No

Step-by-step explanation:

when checking to see if a point satisfies a system of equations

plug in x and y values from your point into the system

(2, 10)

x y

-3(2) - 4(10) = 4. and. -5.2 + 10 = 2

-6-40 = 4. 4.8. = 2

-46 = 4.

invalid statement. invalid statement

therefore the point (2, 10) does not satisfy this system of equations.

6 0
3 years ago
An electrician charges $130 for a house call and $90 for each hour of work. How much will they charge for 7 hours of
babymother [125]

Answer:

Hope it helps

Step-by-step explanation:

Electricians usually charge between $50 to $100 per hour. For the entire project, you'll spend an average of $323, or within a range between $160 and $508 or more. Both hourly and project rates vary depending on the type of project, license and experience of the service provider.

4 0
2 years ago
Read 2 more answers
Other questions:
  • Aidan has 20 ft of fence with which to build a rectangular dog run. What is the maximum area he can enclose?
    15·1 answer
  • 17.
    8·2 answers
  • The sum of two numbers is 12 and their difference is 20. What is the smaller number?
    14·1 answer
  • Jarron has a piece of chalk tied to the end of a
    14·2 answers
  • A test consists of 10 true or false questions. To pass the test a student must answer at least eight questions correctly. If the
    8·1 answer
  • If you owe your friend $3 and you have $15, which expression would help you find out how much money you would have left?
    8·1 answer
  • Evaluate................
    15·1 answer
  • 3. Which number has the greatest absolute value?<br> A)|-3|<br> B)|-8|<br> C)|2|<br> D)|5|
    8·1 answer
  • Write the equation of this line in y= mx + b form
    6·1 answer
  • How many ways are there to divide $12$ people into a group of $3$, a group of $4$, and a group of $5$, if Henry has to be in the
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!