**Problem Statement:**Suppose the number of babies born each hour at a hospital follows a Poisson distribution with a mean of 2. Find the probability that exactly five babies will be born during a particular 1-hour period at this hospital.**Answer Options:**- 0.036089- 0.001739- 0.000006- 0.004511**Explanation:**The given question involves using the Poisson distribution to calculate the probability of a specific event. The Poisson distribution is used to model the number of times an event occurs in an interval of time or space. The probability of observing exactly $ k $ events in an interval is given by:\[ P(X = k) = \frac{{\lambda^k \cdot e^{-\lambda}}}{k!} \]Where:- $ \lambda $ is the average rate (mean), which is 2 in this case.- $ k $ is the number of events (babies), which is 5.To solve the problem, plug in the values into the Poisson probability formula to calculate the probability for $ k = 5 $.

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Description: **Problem Statement:**Suppose the number of babies born each hour at a hospital follows a Poisson distribution with a mean of 2. Find the probability that exactly five babies will be born during a particular 1-hour period at this hospital.**Answer O

Let 'X' be the no.of babies will be born during a particular 1 hour period given,…

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Suppose the number of babies born each hour at a hospital has a Poisson distribution with a mean of 2. Find the probability that exactly five babies will be born during a particular 1-hour period at this hospital.

Suppose the number of babies born each hour at a hospital has a Poisson distribution with a mean of 2. Find the probability that exactly five babies will be born during a particular 1-hour period at this hospital.

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Binomial Distribution

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Question

**Problem Statement:**

Suppose the number of babies born each hour at a hospital follows a Poisson distribution with a mean of 2. Find the probability that exactly five babies will be born during a particular 1-hour period at this hospital.

**Answer Options:**

- 0.036089
- 0.001739
- 0.000006
- 0.004511

**Explanation:**

The given question involves using the Poisson distribution to calculate the probability of a specific event. The Poisson distribution is used to model the number of times an event occurs in an interval of time or space. The probability of observing exactly $ k $ events in an interval is given by:

\[ P(X = k) = \frac{{\lambda^k \cdot e^{-\lambda}}}{k!} \]

Where:
- $ \lambda $ is the average rate (mean), which is 2 in this case.
- $ k $ is the number of events (babies), which is 5.

To solve the problem, plug in the values into the Poisson probability formula to calculate the probability for $ k = 5 $.

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