Arrivals to a bank automated teller machine (ATM) are distributed according to a Poisson distribution with...

Question

Question

Arrivals to a bank automated teller machine (ATM) are distributed according to a Poisson distribution with...

Arrivals to a bank automated teller machine (ATM) are distributed according to a Poisson distribution with a mean equal to five per 10 minutes.
Determine the probability that in a given 10-minute segment, two customers will arrive at the ATM.

a. 0.0842

b.0.1247

c.0.0028

d. 0.9942

what is the probability that fewer than two customers will arrive in a 30 minutes segment?

a. 0.0028

b. 0.0000

c. 0.0842

d. 0.9942

business finance

Add a comment Improve this question Transcribed image text

Answer 1

Answer #1

Formula for poisson distribution is (e^-u * u^x)/x!

Where e = 2.718, u is mean which is 5 and x is 2 as per question.

Substitute the values

e^ -5 = 0.006741

5^2 = 25

Probability= (0.006741*25)/2 = 0.0842

Similarly fewer than 2 means per 30 minutes means (2/3) which is 0 in 10 minutes. Hence value is 0.

Add a comment

Answer 2

Similar Homework Help Questions

Arrivals to a bank automated teller machine (ATM) are distributed according to a Poisson distribution with...

Arrivals to a bank automated teller machine (ATM) are distributed according to a Poisson distribution with a mean equal to four per 5 minutes. Complete parts a and b below. a. Determine the probability that in a given -minute segment, will arrive at the ATM. The probability is nothing. (Round to four decimal places as needed.) b. What is the probability that fewer than customers will arrive in a -minute segment? The probability is
Arrivals to a bank automated teller machine (ATM) are distributed according to a Poisson distribution with...

Arrivals to a bank automated teller machine (ATM) are distributed according to a Poisson distribution with a mean equal to per minutes. Complete parts six 10 a and b below. Click here to view page 1 of the table of Poisson probabilities.1 Click here to view page 2 of the table of Poisson probabilities.2 Click here to view page 3 of the table of Poisson probabilities.3 Click here to view page 4 of the table of Poisson probabilities.4 Click here...
7. An urn contains nine blue balls and six yellow balls. If five balls are selected...

7. An urn contains nine blue balls and six yellow balls. If five balls are selected randomly without being replaced probability that of the balls selected, one of them will be blue and four of them will be yellow? (2 points) N-15 n=5 8. The mean number of errors per page made by a member of the word processing pool for a large company is thought 2.6 with the number of errors distributed according to a Poisson distribution. If a...

The time between arrivals of customers at an automatic teller machine is an exponential random variable...

The time between arrivals of customers at an automatic teller machine is an exponential random variable with a mean of 5 minutes. A) What is the probability that more than three customers arrive in 10 minutes? B) What is the probability that the time until the 6th customer arrives is less than 5 minutes?
Problem 15-1 Willow Brook National Bank operates a drive-up teller window that allows customers to complete...

Problem 15-1 Willow Brook National Bank operates a drive-up teller window that allows customers to complete bank transactions without getting out of their cars. On weekday mornings, arrivals to the drive-up teller window occur at random, with an arrival rate of 24 customers per hour or 0.4 customers per minute. What is the mean or expected number of customers that will arrive in a five-minute period? λ = per five minute period Assume that the Poisson probability distribution can be used...
Customers arrive at a service window according to Poisson process with an average of 0.2 per minute. What is probability that the time between two successive arrivals is less than 6 minutes? (Round your answer to four decimal places)

Customers arrive at a service window according to Poisson process with an average of 0.2 per minute. What is probability that the time between two successive arrivals is less than 6 minutes?

A car wash has one automatic car wash machine. Cars arrive according to a Poisson process...

A car wash has one automatic car wash machine. Cars arrive according to a Poisson process at an average rate of 5 every 30 minutes. The car wash machine can serve customers according to a Poisson distribution with a mean of 0.25 cars per minute. What is the probability that there is no car waiting to be served?
30 customers per hour arrive at a bank on average. These arrivals are independent. There are...

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
I need matlab code for solving this problem Clients arrive to a certain bank according to a Poisson Process. There is a...

I need matlab code for solving this problem Clients arrive to a certain bank according to a Poisson Process. There is a single bank teller in the bank and serving to the clients. In that MIM/1 queieing system; clients arrive with A rate 8 clients per minute. The bank teller serves them with rate u 10 clients per minute. Simulate this queing system for 10, 100, 500, 1000 and 2000 clients. Find the mean waiting time in the queue and...

Many of a bank’s customers use its automatic teller machine to transact business after normal banking...

Many of a bank’s customers use its automatic teller machine to transact business after normal banking hours. During the early evening hours in the summer months, customers arrive at a certain location at the rate of one every other minute. This can be modeled using a Poisson distribution. Each customer spends an average of 83 seconds completing his or her transactions. Transaction time is exponentially distributed. a. Determine the average time customers spend at the machine, including waiting in line...

Arrivals to a bank automated teller machine (ATM) are distributed according to a Poisson distribution with...

Homework Answers

Add Answer to:
Arrivals to a bank automated teller machine (ATM) are distributed according to a Poisson distribution with...

Post as a guest

Earn Coins