Question

At a 24-hour computer repair facility broken-down computers arrive at an average rate of 3 per...

  1. At a 24-hour computer repair facility broken-down computers arrive at an average rate of 3 per day, Poisson distributed.
    1. What is the probability that on a given day no computers arrive for repair?
    2. What is the probability that on a given day at least 3 computers arrive for repair?
    3. What is the distribution of the time between arrivals of computers to this facility and what is the average time between arrivals?
    4. On one particular day no computer has arrived for repair until noon. What is your best estimate of when the next computer will arrive for repair? Hint: forgetfulness property of the exponential distribution.
    5. Suppose a computer has just arrived for repair. What is the probability that the next one will not arrive for at least another 5 hours?
Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

a) probability that on a given day no computers arrive for repair =e-3*30/0! =0.0498

b) probability that on a given day at least 3 computers arrive for repair =P(X>=3) =1-P(X<=2)

=1-(P(X=0)+P(X=1)+P(X=2)) =1-(e-3*30/0!+e-3*31/1!+e-3*32/2!) =0.8647

c)

distribution of the time between arrivals of computers to this facility is exponential with mean time between arrival =1/3 days

or (24/3) =8 hours

d)

best estimate for  next computer will arrive for repair =* hour after noon or at 8.00 pm

e)

probability that the next one will not arrive for at least another 5 hours =P(T>5)=e-5/8 =0.5353

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
At an urgent care facility, patients arrive at an average rate of one patient every five...
At an urgent care facility, patients arrive at an average rate of one patient every five minutes. Assume that the duration between arrivals is exponentially distributed. (Round your answers to four decimal places.) a. Find the probability that the time between two successive visits to the urgent care facility is less than four minutes. b. Find the probability that the time between two successive visits to the urgent care facility is more than 16 minutes. c. If 10 minutes have...
Vehicles arrive at the Bun-and-Run drive-thru at a Poisson rate of 10 per hour. On average,...
Vehicles arrive at the Bun-and-Run drive-thru at a Poisson rate of 10 per hour. On average, 25% of these vehicles are trucks. Calculate the probability that at least 2 trucks arrive between noon and 2:00 PM. (Round to 3 decimals)
At an airport domestic flight arrive according to a Poisson distribution with rate 5 per hour,...
At an airport domestic flight arrive according to a Poisson distribution with rate 5 per hour, and international flights arrive according to a Poisson distribution with rate 1 per hour. What is the probability that the time between third and fourth flight arrivals is more than 15 minutes?
On Fridays at KK airport in Lusaka, airplanes arrive at an average of 3 for the...
On Fridays at KK airport in Lusaka, airplanes arrive at an average of 3 for the one hour period 13 00 hours to 14 00 hours. If these arrivals are distributed according to the Poisson probability distribution, what are the probability that either one or two airplanes will arrive between 13.00 hours and 14 00 hours next Friday?   
Customers arrive at a grocery store at an average of 2.2 per minute. Assume that the...
Customers arrive at a grocery store at an average of 2.2 per minute. Assume that the number of arrivals in a minute follows the Poisson distribution. Provide answers to the following to 3 decimal places. What is the probability that at least seven customers arrive in three minutes, given that exactly two arrive in the first minute?
Customers arrive at a bank according to a Poisson process with rate 10 per hour. Given...
Customers arrive at a bank according to a Poisson process with rate 10 per hour. Given that two customers arrived in the first 5 minutes, what is the probability that (a) both arrived in the first 2 minutes. (b) at least one arrived in the first 2 minutes.
Soltan Security is a security company that retains a service crew to repair its vehicles. The...
Soltan Security is a security company that retains a service crew to repair its vehicles. The vehicle breakdowns occur at a rate of 3 per day, and follow a Poisson process. The crew can service an average of 8 vehicles per day, with a repair time distribution that resembles the exponential distribution. a) What is the utilization rate of the service system? b) What is the average downtime for a vehicle that is broken down? c)How many vehicles are waiting...
Each sweat shop worker at a computer factory can put together 4.7 computers per hour on...
Each sweat shop worker at a computer factory can put together 4.7 computers per hour on average with a standard deviation of 0.9 computers. 6 workers are randomly selected to work the next shift at the factory. Round all answers to 4 decimal places where possible and assume a normal distribution. What is the distribution of X? X ~ N(____________,_____________) What is the distribution of ¯x? ¯x ~ N(______________,_____________) What is the distribution of ∑x ? ∑x ~ N(_____________,_____________) If...
Each sweat shop worker at a computer factory can put together 4 computers per hour on...
Each sweat shop worker at a computer factory can put together 4 computers per hour on average with a standard deviation of 0.7 computers. 7 workers are randomly selected to work the next shift at the factory. Round all answers to 4 decimal places where possible and assume a normal distribution. What is the distribution of XX? XX ~ N(,) What is the distribution of ¯xx¯? ¯xx¯ ~ N(,) What is the distribution of ∑x∑x? ∑x∑x ~ N(,) If one...
Each sweat shop worker at a computer factory can put together 4.7 computers per hour on...
Each sweat shop worker at a computer factory can put together 4.7 computers per hour on average with a standard deviation of 0.7 computers. 48 workers are randomly selected to work the next shift at the factory. Round all answers to 4 decimal places where possible and assume a normal distribution. What is the distribution of XX? XX ~ N(,) What is the distribution of ¯xx¯? ¯xx¯ ~ N(,) What is the distribution of ∑x∑x? ∑x∑x ~ N(,) If one...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT