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 48 customers per hour or 0.8 customers per minute. Assume the Poisson probability distribution can be used to describe the arrival process.(a) What is the mean or expected number of customers that will arrive in a five-minute period?(b) Use the arrival rate in part (a) and compute the probabilities that exactly 0, 1, 2, and 3 customers will arrive during a five-minute period. (Round your answers to four decimal places.)X0123P(x)(c) Delays are expected if more than three customers arrive during any five-minute period. What is the probability that delays will occur? (Round your answer to four decimal places.)

The mean or average number of events occurring in a given time period follows the Poisson…

Answered: Villow Brook National Bank operates a…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Based on historical data, your manager believes that 34% of the company's orders come from first-time customers. A random sample of 168 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is between 0.28 and 0.41? (Enter your answer as a number accurate to 4 decimal places.)
A bag contains 2 red balls worth £3, 2 blue balls worth £2 and 5 green balls worth £0. You pick 1 ball out of the bag (without replacement). What the expected value of earnings from playing this game once (3 decimal places).
Based on historical data, your manager believes that 29% of the company's orders come from first-time customers. A random sample of 147 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is less than 0.33?Answer = (Enter your answer as a number accurate to 4 decimal places.)
A group of botanists is studying the distribution of carnations in a field. The field is divided into a number of equal sized squares. The mean number of carnations per square is assumed to be 3. The carnations are distributed randomly throughout the field. Find the probability that: (b) (i) there will be more than two carnations. (ii) either five or six carnations.
For 10 percent of the products in a category, a firm fails to satisfy all demand during themonth. What is its in-stock probability?
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Based on historical data, your manager believes that 29% of the company's orders come from first-time customers. A random sample of 151 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is less than 0.33?Answer = (Enter your answer as a number accurate to 4 decimal places.)
In a 24-hour call center, complaints arrive at a mean rate of 1 complaint every 3 hours. (a) Find the probability that there are at most 3 complaints in the past 10 hours. (b) A day is “doomed” if there are at least 6 complaints. Each day, an inspector counts the number of complaints at the end of the day and determines whether the day was doomed. Find the probability that the inspector has worked for 7 days when he records the 3rd doomed day. (c) Find the probability that there are at least 2 complaints in the past 12 hours given that there are at most 5 complaints in the past 12 hours
Calculate the expected value of x, the sum of the scores, when two dice are rolled.
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 30 customers per hour or 0.5 customers per minute. Let's assume that the service times for the drive-up teller follow an exponential probability distribution with a service rate of 45 customers per hour, or 0.75 customers per minute. Determine the following operating characteristics for the system. (Round your answers to four decimal places.) (a) The probability that no customers are in the system 1353 (b) The average number of customers waiting 1786 (c) The average number of customers in the system 1.25 (d) The average time (in min) a customer spends waiting 4.2 X min (e) The average time (in min) a customer spends in the system x min 1 (f) The probability that arriving customers will have to wait for service 73 X
Cal Poly Pomona found that 15% of its students withdraw without completing Calculus I course. Assume that 30 students registered for the course. Compute the probability that exactly 6 students will withdraw. Leave your answer in four decimal places.

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