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
Basile [38]
3 years ago
8

Assume that power surges occur as a Poisson process with rate 3 per hour. These events cause damage to a computer, thus a specia

l protecting unit has been designed. That unit now has to be removed from the system for 10 minutes for service.
(a) Assume that a single disturbance will cause the computer to crash. What is the probability that the system will crash in the coming 10 minutes?
(b) Assume that the computer will survive a single disturbance, but the second such disturbance will cause it to crash. What is, now, the probability that the computer will crash in the coming 10 minutes?
Mathematics
1 answer:
lidiya [134]3 years ago
3 0

Answer:

a) 0.30327

b) 0.07582

Step-by-step explanation:

This is a Poisson distribution problem

Poisson distribution probability function is given as

P(X = x) = (e^-λ)(λˣ)/x!

where λ = mean = 3 power surges per hour

x = variable whose probability is required

a) If a single disturbance in 10 minutes will crash the computer, what is the probability of the computer crashing, that is probability of a single disturbance (power surge) in 10 minutes?

λ = 3 disturbances per hour = 1 disturbance per 20 minutes = 0.5 disturbance per 10 minutes.

P(X = x) = (e^-λ)(λˣ)/x!

λ = 0.5 disturbance per 10 minutes

x = 1 disturbance per 10 minutes

P(X = 1) = (e^-0.5)(0.5¹)/1! = (e⁻⁰•⁵)(0.5)/1!

= 0.30327

b) If two disturbances in 10 minutes will crash the computer, what is the probability of the computer crashing, that is probability of two disturbances (power surges) in 10 minutes?

λ = 3 disturbances per hour = 1 disturbance per 20 minutes = 0.5 disturbance per 10 minutes.

P(X = x) = (e^-λ)(λˣ)/x!

λ = 0.5 disturbance per 10 minutes

x = 2 disturbance per 10 minutes

P(X = 2) = (e^-0.5)(0.5²)/2! = (e⁻⁰•⁵)(0.25)/2!

= 0.07582

Hope this Helps!!!

You might be interested in
If the angles of a triangle are in the ratio 3:4:2 find the value of all triangle​
Nata [24]

Answer:

Step-by-step explanation:

If the ratio of triangle = 3:4:2

Total ratio = 3+4+2 = 9

The sum of angle in a triangle is 180°

1st angle= 3/9 × 180 = 2 × 20 = 60°

2nd angle= 4/9 × 180 = 4 × 20 = 80°

3rd angle= 2/9 × 180 = 2 × 20 = 40°

6 0
3 years ago
A vase can hold 9 flowers. If a florist had 878 flowers she wanted to put equally into vases, how many flowers would be in the l
zavuch27 [327]
There are 5 flowers in the last vase because you divide 878 by 9 and get 97 and then you have 5 leftover
3 0
3 years ago
Read 2 more answers
A manufacturing process makes rods that vary slightly in length but follow a normal distribution with mean length 25 cm and stan
Galina-37 [17]

Answer:

The probability of randomly selecting a rod that is shorter than 22 cm

P(X<22)  = 0.1251

Step-by-step explanation:

<u><em>Step(i):</em></u>-

Given mean of the Population = 25cm

Given standard deviation of the Population = 2.60

Let 'x' be the random variable in normal distribution

Given x=22

Z = \frac{x-mean }{S.D} = \frac{22-25}{2.60} = -1.15

<u><em>Step(ii):</em></u>-

The probability of randomly selecting a rod that is shorter than 22 cm

P(X<22) = P( Z<-1.15)

             = 1-P(Z>1.15)

             =  1-( 0.5+A(1.15)

             =  0.5 - A(1.15)

             = 0.5 - 0.3749

             = 0.1251

The probability of randomly selecting a rod that is shorter than 22 cm

P(X<22)  = 0.1251

7 0
3 years ago
In my fish tank, the ratio of red fish to blue fish is 1:5. There are 15 blue fish. How many red fish are there?
ElenaW [278]

Answer:

there are 3 red fish

Step-by-step explanation:

1:5

_:15

5 times 3 =15

so 1 times 3 =3

4 0
4 years ago
Read 2 more answers
Help help help pls help
Brilliant_brown [7]

AB = 6.1

\sin(c)  =  \frac{ab}{x}  \\  \\ ab = 7.7 \sin(52)  \\ ab = 6.06

6 0
3 years ago
Read 2 more answers
Other questions:
  • Vertex on the graph of the equation y=3x^2 + 6x + 1
    8·1 answer
  • How do you solve this equation, 5s^2-14s-3=0
    15·1 answer
  • How do you solve the system of y=x and x-4y=0
    14·1 answer
  • There are 7 times as many males as females on the maths course at university. What fraction of the course are male? Give your an
    14·1 answer
  • At Riverglen Jr High, 30 girls tried out for the basket ball team and 12 were selected. As for the boys, 40 tried out and 16 wer
    6·1 answer
  • A certain companies main source of income is a mobile app. The companies annual profit (in millions of dollars) as a function of
    9·1 answer
  • What to do on 9 and 10
    9·1 answer
  • Which is the same as dividing a number by 10?
    13·2 answers
  • Which is least? 1.26 ÷ 0.3 OR 7.84 ÷ 5.6
    11·2 answers
  • The elgebaric expression for 5y to the product of a and b.
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!