Question

The average number of customers arriving at a bank branch is eight per hour. Assume that...

The average number of customers arriving at a bank branch is eight per hour. Assume that customer arrivals follow a Poisson process. The bank opens at 9:00 am in the morning. Answer the following questions accordingly.

a) What is the probability that the first customer will arrive after 9:10 am?

b) Suppose that it is now 9:15 and the first customer has arrived at 9:12 am. What is the probability that the second customer will arrive after 9:25 am?

c) What is the probability that the third customer arrives exactly at 9:45 am?

d) What is the probability that exactly three customers arrive by 9:45 am?

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

Note in each case, we computed rate parameter of Poisson RV by considering the appropriate time intervals in minutes unit and given rate of 8 per hr as 8 per 60 mins.

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
Let average number of customers arriving at a bank is 40/hour. Find the probability that exactly...
Let average number of customers arriving at a bank is 40/hour. Find the probability that exactly 6 customers will arrive at the bank during a 15 minute period.
Suppose that customers arrive at a bank at a rate of 10 per hour. Assume that...
Suppose that customers arrive at a bank at a rate of 10 per hour. Assume that the number of customer arrivals X follows a Poisson distribution. Find the probability of more than 25 people arriving within the next two hours using the Poisson mass function. Find the probability of more than 25 people arriving within the next two hours using the normal approximation to the Poisson. Compute the percent relative difference between the exact probability computed in part 1 and...
Suppose that customers arrive at a bank at a rate of 10 per hour. Assume that...
Suppose that customers arrive at a bank at a rate of 10 per hour. Assume that the number of customer arrivals X follows a Poisson distribution. 1. Find the probability of more than 25 people arriving within the next two hours using the Poisson mass function. 2. Find the probability of more than 25 people arriving within the next two hours using the normal approximation to the Poisson. 3. Compute the percent relative difference between the exact probability computed in...
Customers are arriving to a shop according to Poisson process with mean 2.7 customers/hour. What is...
Customers are arriving to a shop according to Poisson process with mean 2.7 customers/hour. What is the probability that the next customer will arrive after 23 minutes but before 38 minutes?
Customers arrive to a savings bank according to a Poisson distribution with mean 3 per hour....
Customers arrive to a savings bank according to a Poisson distribution with mean 3 per hour. Then, they either complete a transaction with a bank teller or meet with a financial officer, and leave the bank when they are done. What is the probability that exactly 2 customers arrive in the next three hours? What is the probability that at least 3 customers arrive in the next two hours? What is the probability that nobody arrives in the next 30...
Individual customers arrive at a coffee shop after it opens at 6 AM. The number of...
Individual customers arrive at a coffee shop after it opens at 6 AM. The number of customers arriving by 7AM has a Poisson distribution with parameter λ = 10. 25% of the customers buy a single donut and coffee, and 75% just buy coffee. Each customer acts independently. Answer the following: a.What are the two random variables described above and what are their probability mass functions? b.What is the probability that exactly five customers arrive by 7AM? c.If 10 customers...
B. Customers arrive at a restaurant according to a Poisson process. On the average, a customer...
B. Customers arrive at a restaurant according to a Poisson process. On the average, a customer arrives every half hour. (a) What is the probability that, 1 hour after opening, there at least one customer has arrived? (b) What is the probability that at least 2 customers have arrived?
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 bank according to a Poisson process with rate 20 customers per hour. The...
Customers arrive at bank according to a Poisson process with rate 20 customers per hour. The bank lobby has enough space for 10 customers. When the lobby is full, an arriving customers goes to another branch and is lost. The bank manager assigns one teller to customer service as long as the number of customers in the lobby is 3 or less. She assigns two tellers if the number is more than 3 but less than 8. Otherwise she assigns...
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.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT