**Problem Statement:**Records show that the average number of births at Highland Hospital per hour is 8.1. Find the probability of between 5 and 7 births at Highland Hospital (endpoints included) in a given hour.Round your answer to three decimal places, and include all written work using the probability mass function. Do not use graphing calculator distribution commands or R.**Input Fields:**- [ ] (Input Box)**Buttons:**- Add Work- Submit Question---**Explanation:**To solve this problem, you need to use the Poisson probability mass function (PMF), which is suitable for modeling the number of events in a fixed interval of time given a known average rate of occurrence.The PMF of a Poisson distribution is given by:\[ P(X = k) = \frac{e^{-\lambda} \cdot \lambda^k}{k!} \]where:- \( \lambda \) is the average number of events (births) in a given time period (8.1 in this case),- \( k \) is the actual number of events you want to find the probability for (5, 6, or 7 births),- \( e \) is the base of the natural logarithm (approximately equal to 2.71828).To find the probability of between 5 and 7 births, you need to calculate:\[ P(5 \le X \le 7) = P(X = 5) + P(X = 6) + P(X = 7) \]Calculate each term using the PMF formula and add the probabilities to get the final result, rounding the answer to three decimal places.

Records show that the average number of births at Highland Hospital per hour is 8.1. Find the probability of between 5 and 7 births at Highland Hospital (endpoints included) in a given hour. Round your answer to three decimal places, and include all written work using the probability mass function. Do not use graphing calculator distribution commands or R. Add Work Submit Question

Records show that the average number of births at Highland Hospital per hour is 8.1. Find the probability of between 5 and 7 births at Highland Hospital (endpoints included) in a given hour. Round your answer to three decimal places, and include all written work using the probability mass function. Do not use graphing calculator distribution commands or R. Add Work Submit Question

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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