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**Title: Probability Analysis of Candy Weights** **Introduction** This exercise involves analyzing the weights of candies, which are normally distributed. The given parameters for this distribution are: - Sample size (\( n \)): 469 - Mean weight (\( \mu \)): 0.8556 g - Standard deviation (\( \sigma \)): 0.051 g **Objective** We aim to find the probability related to the weight of the candies exceeding a certain value. **Problem Statement** (a) If one candy is randomly selected, we need to find the probability that its weight exceeds 0.8542 g. - **Formula:** The probability is determined using the properties of the normal distribution and is expressed to four decimal places. (b) If 469 candies are randomly selected, we calculate the probability that the mean weight is at least 0.8542 g. - **Formula:** \( P(X \geq 0.8542) \) **Analysis** For part (a), use the standard normal distribution to find the probability of a single candy weighing more than 0.8542 g. For part (b), apply the Central Limit Theorem to determine the probability that the sample mean is greater than or equal to 0.8542 g for 469 candies. **Conclusion** Understanding these probabilities helps in quality control and assessment of candy production processes, ensuring the weights meet the expected standards.

**Title: Probability Analysis of Candy Weights** **Introduction** This exercise involves analyzing the weights of candies, which are normally distributed. The given parameters for this distribution are: - Sample size (\( n \)): 469 - Mean weight (\( \mu \)): 0.8556 g - Standard deviation (\( \sigma \)): 0.051 g **Objective** We aim to find the probability related to the weight of the candies exceeding a certain value. **Problem Statement** (a) If one candy is randomly selected, we need to find the probability that its weight exceeds 0.8542 g. - **Formula:** The probability is determined using the properties of the normal distribution and is expressed to four decimal places. (b) If 469 candies are randomly selected, we calculate the probability that the mean weight is at least 0.8542 g. - **Formula:** \( P(X \geq 0.8542) \) **Analysis** For part (a), use the standard normal distribution to find the probability of a single candy weighing more than 0.8542 g. For part (b), apply the Central Limit Theorem to determine the probability that the sample mean is greater than or equal to 0.8542 g for 469 candies. **Conclusion** Understanding these probabilities helps in quality control and assessment of candy production processes, ensuring the weights meet the expected standards.

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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**Title: Probability Analysis of Candy Weights** **Introduction** This exercise involves analyzing the weights of candies, which are normally distributed. The given parameters for this distribution are: - Sample size (\( n \)): 469 - Mean weight (\( \mu \)): 0.8556 g - Standard deviation (\( \sigma \)): 0.051 g **Objective** We aim to find the probability related to the weight of the candies exceeding a certain value. **Problem Statement** (a) If one candy is randomly selected, we need to find the probability that its weight exceeds 0.8542 g. - **Formula:** The probability is determined using the properties of the normal distribution and is expressed to four decimal places. (b) If 469 candies are randomly selected, we calculate the probability that the mean weight is at least 0.8542 g. - **Formula:** \( P(X \geq 0.8542) \) **Analysis** For part (a), use the standard normal distribution to find the probability of a single candy weighing more than 0.8542 g. For part (b), apply the Central Limit Theorem to determine the probability that the sample mean is greater than or equal to 0.8542 g for 469 candies. **Conclusion** Understanding these probabilities helps in quality control and assessment of candy production processes, ensuring the weights meet the expected standards.
Transcribed Image Text:**Title: Probability Analysis of Candy Weights** **Introduction** This exercise involves analyzing the weights of candies, which are normally distributed. The given parameters for this distribution are: - Sample size (\( n \)): 469 - Mean weight (\( \mu \)): 0.8556 g - Standard deviation (\( \sigma \)): 0.051 g **Objective** We aim to find the probability related to the weight of the candies exceeding a certain value. **Problem Statement** (a) If one candy is randomly selected, we need to find the probability that its weight exceeds 0.8542 g. - **Formula:** The probability is determined using the properties of the normal distribution and is expressed to four decimal places. (b) If 469 candies are randomly selected, we calculate the probability that the mean weight is at least 0.8542 g. - **Formula:** \( P(X \geq 0.8542) \) **Analysis** For part (a), use the standard normal distribution to find the probability of a single candy weighing more than 0.8542 g. For part (b), apply the Central Limit Theorem to determine the probability that the sample mean is greater than or equal to 0.8542 g for 469 candies. **Conclusion** Understanding these probabilities helps in quality control and assessment of candy production processes, ensuring the weights meet the expected standards.
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