Question
In: Statistics and Probability
In a lake, Peter catches fishes in an average rate of 3 fishes per hour. (Using...
In a lake, Peter catches fishes in an average rate of 3 fishes
per hour. (Using Poisson distribution, 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 the 2nd fish between 9:30 and
9:50AM?
Solutions
orchestra answered 1 year agoRelated Solutions
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...
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.]
In a barber, the rate for the number of customers is 3 per hour. On average, the barber can serve customers at a rate of one every 15 minutes.
In a barber, the rate for the number of customers is 3 per hour. On average, the barber can serve customers at a rate of one every 15 minutes.A) Find an average number of the customers in the barber (system) and queue?B) Find average waiting time in the barber and queue?C) What is the probability that the barber be empty?D) What is the probability that exactly 2 customers present in the system? C) with which probability that the number of...
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...
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)...
4. Customers enter a store at a rate of 3 customers per hour. a) Compute the...
4. Customers enter a store at a rate of 3 customers per
hour.
a) Compute the probability that at least two, but no more than
five customers enter the store in a given hour.
b) Compute the probability that it takes more than 30 minutes
for the first customer to enter the store this hour.
c) Suppose you know that exactly 1 customer entered the store
during a given hour. Compute the probability that the customer
entered the store between...
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