The number of customers who enter a bank is thought to be Poisson distributed with a mean equal to 10 per hour. What are the chances that no customers will arrive in a 15-minute period?

Question

BlackTom AI · Accepted Answer

We start by identifying the Poisson parameter for the 15-minute interval. The bank sees an average of 10 customers per hour, so for a 0.25-hour period the expected number of arrivals (λ) is 10 × 0.25 = 2.5.

Option 1: 0.0821. This value matches the probability of observing zero arrivals in a Poisson distribution with λ = 2.5, which is P(N=0) = e^{-λ} = e^{-2.5} ≈ 0.082085. Rounding to four decimals gives 0.0821, so this option is numerically correct.

Option 2: Approximately zero. While probabilities for rare events can be small, P(N=0) with λ = 2.5 is not near zero; it is about 8.2%. Describing it as approximately zero would be misleading because there is a definite non-negligible chance.

Option 3: 0.0250. This value does not correspond to P(N=0) for λ = 2.5. A probability of 0.0250 might arise from a different event or a miscalculation, but it does not reflect the zero-arrival probability for this Poisson parameter.

Option 4: 0.0067. This is even smaller and further from the actual P(N=0) for λ = 2.5. Since e^{-2.5} ≈ 0.0821, 0.0067 represents a probability far removed from the correct zero-arrival probability for the given rate and interval.

OSC 2030-009 Fall 2025 Exam 1

The number of customers who enter a bank is thought to be Poisson distributed with a mean equal to 10 per hour. What are the chances that no customers will arrive in a 15-minute period?

View Explanation

Log in for full answers

Similar Questions

位置13的问题 A property of the Poisson distribution is that the mean equals the 题库 1/1[input].

In the textile industry, a manufacturer is interested in the number of blemishes or flaws occurring in each 100 feet of material. The probability distribution that has the greatest chance of applying to this situation is the

The number of visible defects on a product container is thought to be Poisson distributed with a mean equal to 3.5 defects per container. Based on this, the probability that 2 containers will contain a total of less than 2 defects is:

The number of weeds that remain living after a specific chemical has been applied averages 1.3 per square yard and follows a Poisson distribution. Based on this, what is the probability that a 3-square yard section will contain less than 4 weeds?

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler