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10. The mean weight of a group of boys is 175 lb, with a standard deviation of 12 lb. If the weights are normally distributed, what percent of the boys from the group weigh between 193 and 202 lb? Round your answer to one decimal place. a. 43.3% b. 48.8% c. 92.1% d. 5.5% e. 7.9% Contemporary Mathematics (MAT 134) Q Search D PRE #]

10. The mean weight of a group of boys is 175 lb, with a standard deviation of 12 lb. If the weights are normally distributed, what percent of the boys from the group weigh between 193 and 202 lb? Round your answer to one decimal place. a. 43.3% b. 48.8% c. 92.1% d. 5.5% e. 7.9% Contemporary Mathematics (MAT 134) Q Search D PRE #]

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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### Educational Content: Example Problem in Probability and Statistics **Problem Statement:** A group of boys has a mean weight of 175 pounds, with a standard deviation of 12 pounds. Assuming that the weights are normally distributed, calculate the percentage of the boys whose weights are between 193 and 202 pounds. Round your answer to one decimal place. **Options:** - a. 43.3% - b. 48.8% - c. 92.1% - d. 5.5% - e. 7.9% --- **Explanation:** To solve this problem, you would typically use the properties of the normal distribution. The mean (μ) is given as 175 lb, and the standard deviation (σ) is 12 lb. To find out what percentage of boys weigh between 193 lb and 202 lb, you would: 1. Calculate the z-scores for 193 and 202. - Z = (X - μ) / σ - For 193 lb: Z193 = (193 - 175) / 12 - For 202 lb: Z202 = (202 - 175) / 12 2. Use a standard normal distribution table or a calculator to find the percentage associated with each z-score. 3. The percentage of boys weighing between the two values is the difference between the two percentages found. --- **Note:** This exercise requires understanding of the normal distribution curve and knowledge on how to use z-scores in probability calculations.
Transcribed Image Text:### Educational Content: Example Problem in Probability and Statistics **Problem Statement:** A group of boys has a mean weight of 175 pounds, with a standard deviation of 12 pounds. Assuming that the weights are normally distributed, calculate the percentage of the boys whose weights are between 193 and 202 pounds. Round your answer to one decimal place. **Options:** - a. 43.3% - b. 48.8% - c. 92.1% - d. 5.5% - e. 7.9% --- **Explanation:** To solve this problem, you would typically use the properties of the normal distribution. The mean (μ) is given as 175 lb, and the standard deviation (σ) is 12 lb. To find out what percentage of boys weigh between 193 lb and 202 lb, you would: 1. Calculate the z-scores for 193 and 202. - Z = (X - μ) / σ - For 193 lb: Z193 = (193 - 175) / 12 - For 202 lb: Z202 = (202 - 175) / 12 2. Use a standard normal distribution table or a calculator to find the percentage associated with each z-score. 3. The percentage of boys weighing between the two values is the difference between the two percentages found. --- **Note:** This exercise requires understanding of the normal distribution curve and knowledge on how to use z-scores in probability calculations.
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