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robability. An airline knows from experience that the distribution of the number of suitcases that get lost each week on a certain route is approximately normal with µ = 15.5 and o = 3.6. What is the probability that during a given week the airline will lose between 10 and 20 suitcases? 0.1056 0.4040 0.3944 0.8314

robability. An airline knows from experience that the distribution of the number of suitcases that get lost each week on a certain route is approximately normal with µ = 15.5 and o = 3.6. What is the probability that during a given week the airline will lose between 10 and 20 suitcases? 0.1056 0.4040 0.3944 0.8314

MATLAB: An Introduction with Applications
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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### Find the Indicated Probability An airline knows from experience that the distribution of the number of suitcases that get lost each week on a certain route is approximately normal with mean (μ) = 15.5 and standard deviation (σ) = 3.6. What is the probability that during a given week the airline will lose between 10 and 20 suitcases? #### Answer Choices: - ○ 0.1056 - ○ 0.4040 - ○ 0.3944 - ○ 0.8314 #### Explanation: The problem requires determining the probability that a normally distributed random variable falls between 10 and 20, given a mean (μ) and standard deviation (σ). This can be solved using the standard normal distribution (Z-distribution) and Z-scores. No graphs or diagrams are presented in this image. However, a normal distribution curve can be imagined, centered at the mean (μ) = 15.5, with areas under the curve corresponding to the given probabilities. ### Key Points: 1. **Normal Distribution**: The data follows a bell-shaped, symmetric curve centered around the mean. 2. **Z-score Calculation**: Conversion of the values (10 and 20 in this case) to Z-scores. 3. **Probability Determination**: Use Z-tables or statistical software to find the area under the standard normal curve corresponding to the Z-scores, which represent the probabilities.
Transcribed Image Text:### Find the Indicated Probability An airline knows from experience that the distribution of the number of suitcases that get lost each week on a certain route is approximately normal with mean (μ) = 15.5 and standard deviation (σ) = 3.6. What is the probability that during a given week the airline will lose between 10 and 20 suitcases? #### Answer Choices: - ○ 0.1056 - ○ 0.4040 - ○ 0.3944 - ○ 0.8314 #### Explanation: The problem requires determining the probability that a normally distributed random variable falls between 10 and 20, given a mean (μ) and standard deviation (σ). This can be solved using the standard normal distribution (Z-distribution) and Z-scores. No graphs or diagrams are presented in this image. However, a normal distribution curve can be imagined, centered at the mean (μ) = 15.5, with areas under the curve corresponding to the given probabilities. ### Key Points: 1. **Normal Distribution**: The data follows a bell-shaped, symmetric curve centered around the mean. 2. **Z-score Calculation**: Conversion of the values (10 and 20 in this case) to Z-scores. 3. **Probability Determination**: Use Z-tables or statistical software to find the area under the standard normal curve corresponding to the Z-scores, which represent the probabilities.
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