Ans:
6)mean rate=6 per hour
a)
P(x=3)=exp(-6)*(6^3/3!)
=0.0892
b)
P(x<=3)=P(x=0)+P(x=1)+P(x=2)+P(x=3)
=exp(-6)*(6^0/0!+6^1/1!+6^2/2!+6^3/3!)
=0.1512
c)average number of customers in 2 hour=2*6=12
P(x=10)=exp(-12)*(12^10/10!)=0.1048
6. Customer arrivals at a check out counter have a Poison distribution with an average of...
Customer arrivals at a checkout counter in a department store have a Poisson distribution with an average of seven per hour. For a given hour, find the probability that a. exactly nine customers arrive b. no more than three customers arrive c. at least two customers arrive
Customers arrivals at a checkout counter in a department store per hour have a Poisson distribution with parameter λ = 7. Calculate the probabilities for the following events. (a) (2 points) Exactly seven customers arrive in a random 1-hour period. (b) (4 points) No more than two customers arrive in a random 1-hour period. (c) (4 points) At least three customers arrive in a random 1-hour period.
30 customers per hour arrive at a bank on average. These arrivals are independent. There are employees to help the customers (a) What is the probability that there are more than two customers arrivals within 10 minutes. (b) What is the probability that the next customer to arrive at the bank arrives 2 or more minutes later. Show all work
Customers arrive at a store randomly, following a Poisson distribution at an average rate of 20 per hour. What is the probability of exactly 3 arrivals in a 12 minute period?
A Fast Food drive-through Restaurant with a single check-out counter opens six days a week, but its heaviest day of business is on Saturdays. Customers arrive at an average rate of 20 per hour on Saturdays. Customers can be provided service at the rate of one every two minutes. Assuming Poisson arrivals and exponential service times, find: The average number of customers in line The average time a car waits before being served The average time a customer spends in...
A shop has an average of five customers per hour 5. A shop has an average of five customers per hour (a) Assume that the time T between any two customers' arrivals is an exponential random variable. (b) Assume that the number of customers who arrive during a given time period is Poisson. What (c) Let Y, be exponential random variables modeling the time between the ith and i+1st c What is the probability that no customer arrives in the...
Problem 6 Customers arrive randomly at a checkout counter at the average rate of 20 per hour. a) Determine the probability that the counter is idle b) What is the probability that at least two people are in line awaiting service? Problem'7 Customers shopping at Sprouts Store are both from east and west of Norman. The ones from the east of Norman arrive at the rate of 5 per minute. The ones from the west of Norman arrive at the...
Customers arrive at a local ATM at an average rate of 15 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 5 minutes? b) What is the probability that the next customer will arrive in more than 8 minutes? c) What is the probability that the next customer will...
A children's hospital has reported that an average of 6 patients arrive in the emergency room each hour. Arrivals at this emergency room are known to follow a Poisson probability distribution. a.) What is the probability that exactly 10 patients will arrive in the emergency room between 1:00 pm and 2:00 pm today? b.) What is the probability that no more than 3 patients will arrive in the emergency room between 6:30 pm and 7:30 pm today? c.) What is...
QUESTION 2: Consider a check–out station at a small store with customer arrivals described by a Poisson process with intensity ? = 10 customers per hour. There are two service team members, Tom and Jerry, working one per shift. In Tom’s shift, the service times are exponentially distributed with the mean time equal to 3 minutes, while for Jerry service times are exponentially distributed with the mean time equal to 5 minutes. 1. Find the mean queue length during the...