Question

In: Math

Meteorites randomly strike the earth’s surface at an average rate of 90 meteorites per hour. (a)...

Meteorites randomly strike the earth’s surface at an average rate of 90 meteorites per hour.

(a) Find the probability that at least 4 meteorites strike the earth during a three-minute interval.

(b) Find the probability that the time between two consecutive meteorites striking the earth is greater than 20 seconds. Derive the formulation using the c.d.f., but do not calculate it.

(c) Find the probability that the time until 4 meteorites strike the earth is greater than 2 minutes.

(d) Calculate the expected time until 4 meteorites strike the earth.

I know we use poissons distribution but im having trouble breaking down and understanding this problem.

Solutions

Expert Solution

meteorites randomly strike the earths surface at an average rate of 90 meteorites per hour

milcah answered 7 months ago
Next > < Previous

Related Solutions

If meteorites strike the surface of the moon "at random", the number of meteorite craters per...
If meteorites strike the surface of the moon "at random", the number of meteorite craters per unit area should be a Poisson random variable with parameter Lambda (expected number of craters per unit area). If N=10 units of area are examined and the total number of meteorite craters found is 8, would you accept H_0: lambda=0.5 with alpha=0.68, with the alternative H_1: lambda=1? Evaluate Beta for this test.
Cars and trucks arrive at a gas station randomly and independently of each other, at an average rate of 17.4 and 9.6 per hour, respectively.
  Cars and trucks arrive at a gas station randomly and independently of each other, at an average rate of 17.4 and 9.6 per hour, respectively. Use the Poisson distribution to find the probability that a. more than 5 cars arrive during the next 16 minutes, b. we have to wait more than 21 minutes for the arrival of the third truck (from now), c. the fifth vehicle will take between 17 and 23 minutes (from now) to arrive.
On average, 90 patrons arrive per hour at a hotel lobby (interarrival times are exponential) waiting...
On average, 90 patrons arrive per hour at a hotel lobby (interarrival times are exponential) waiting to check in. At present there are five clerks, and patrons wait in a single line for the first available clerk. The average time for a clerk to service a patron is three minutes (exponentially distributed). Clerks earn $10 per hour, and the hotel assesses a waiting time cost of $20 for each hour that a patron waits in line. If needed, round your...
Jobs are sent to a printer at an average rate of 6 jobs per hour. (a)...
Jobs are sent to a printer at an average rate of 6 jobs per hour. (a) What is the expected time between jobs? [Note: Give the exact answer either in hours or in minutes.] (b) What is the probability that the next job is sent within 4 minutes? [Note: Round the answer to four decimal places.]
Customers arrive at a local ATM at an average rate of 14 per hour. Assume the...
Customers arrive at a local ATM at an average rate of 14 per hour. Assume the time between arrivals follows the exponential probability distribution. Determine the probability that the next customer will arrive in the following time frames. ​a) What is the probability that the next customer will arrive within the next 2 ​minutes? ​b) What is the probability that the next customer will arrive in more than 15 ​minutes? ​c) What is the probability that the next customer will...
Customers enter the camera department of a store at an average rate of five per hour....
Customers enter the camera department of a store at an average rate of five per hour. The department is staffed by one employee, who takes an average of 8.0 minutes to serve each arrival. Assume this is a simple Poisson arrival, exponentially distributed service time situation. (Use the Excel spreadsheet Queue Models.) a-1. As a casual observer, how many people would you expect to see in the camera department (excluding the clerk)? (Round your answer to 2 decimal places.) a-2....
Customers enter the camera department of a store at the average rate of eight per hour....
Customers enter the camera department of a store at the average rate of eight per hour. The department is staffed by one employee, who takes an average of 3.0 minutes to serve each arrival. Assume this is a simple Poisson arrival, exponentially distributed service time situation. Use Exhibit 10.9. a-1. As a casual observer, how many people would you expect to see in the camera department (excluding the clerk)? (Round your answer to 2 decimal places.) a-2. How long would...
In a lake, Peter catches fishes in an average rate of 3 fishes per hour. (Assume...
In a lake, Peter catches fishes in an average rate of 3 fishes per hour. (Assume Peter always catches one fish at a time and the events of catching each fish are independent.) (a) [10 points] At 2:00PM, if it’s known that Peter caught the previous fish at 1:50PM, what is the probability that he will catch the next fish before 2:30PM? Please show step by step process for arriving at such answer (b) [10 points] Assume Peter starts catching...
In a lake, Peter catches fishes in an average rate of 3 fishes per hour. (Assume...
In a lake, Peter catches fishes in an average rate of 3 fishes per hour. (Assume Peter always catches one fish at a time and the events of catching each fish are independent.) (a) At 2:00PM, if it’s known that Peter caught the previous fish at 1:50PM, what is the probability that he will catch the next fish before 2:30PM? (b) Assume Peter starts catching fish at 9:00AM, what is the probability that he will catch the 2nd fish between...
In a lake, Peter catches fishes in an average rate of 3 fishes per hour. (Assume...
In a lake, Peter catches fishes in an average rate of 3 fishes per hour. (Assume Peter always catches one fish at a time and the events of catching each fish are independent.) (a) [10 points] At 2:00PM, if it’s known that Peter caught the previous fish at 1:50PM, what is the probability that he will catch the next fish before 2:30PM? (b) [10 points] Assume Peter starts catching fish at 9:00AM, what is the probability that he will catch...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT