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or more? 0.2546 0.1409 0.7454 0.9506 that a skydiver will be 46 years of

or more? 0.2546 0.1409 0.7454 0.9506 that a skydiver will be 46 years of

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 22PFA
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**Understanding Normal Distribution Through an Example** Let's analyze the following problem to understand normal distribution and probability: --- ### Problem: Bryse is 46 years old. Based on a normal distribution with a mean of 52.8 years and a standard deviation of 10.3 years, what is the probability that a skydiver will be 46 years of age or more? --- #### Options: - A. 0.2546 - B. 0.1409 - C. 0.7454 - D. 0.9506 --- **Explanation:** This problem requires us to determine the probability that a skydiver’s age is 46 years or older, given the age distribution is normal with specified parameters. 1. **Understand the Mean and Standard Deviation:** - The mean (average) age is 52.8 years. - The standard deviation, which measures the variation or dispersion of ages from the mean, is 10.3 years. 2. **Calculate the Z-Score:** - Z = \( \frac{X - \mu}{\sigma} \) - Where X is the value we are interested in (46 years), μ is the mean (52.8 years), and σ is the standard deviation (10.3 years). 3. **Look up the Z-Score in a Standard Normal Distribution Table:** - The Z-Score will help us find the probability of a value occurring within a normal distribution. 4. **Determine the Correct Probability:** - Finally, use the Z-score to find the probability and correlate it with the given choices. **Graph Interpretation:** To explain this concept, we visualize it using a bell curve. The mean (52.8 years) is at the center, and as we move left or right, the curve illustrates the distribution of ages. The area under the curve up to a certain point corresponds to the probability. By solving this, you will better understand how to use normal distribution and standard deviation to find the probability of a certain range of outcomes. --- For a detailed step-by-step solution, refer to our section on **Normal Distributions and Probability Calculations.**
Transcribed Image Text:**Understanding Normal Distribution Through an Example** Let's analyze the following problem to understand normal distribution and probability: --- ### Problem: Bryse is 46 years old. Based on a normal distribution with a mean of 52.8 years and a standard deviation of 10.3 years, what is the probability that a skydiver will be 46 years of age or more? --- #### Options: - A. 0.2546 - B. 0.1409 - C. 0.7454 - D. 0.9506 --- **Explanation:** This problem requires us to determine the probability that a skydiver’s age is 46 years or older, given the age distribution is normal with specified parameters. 1. **Understand the Mean and Standard Deviation:** - The mean (average) age is 52.8 years. - The standard deviation, which measures the variation or dispersion of ages from the mean, is 10.3 years. 2. **Calculate the Z-Score:** - Z = \( \frac{X - \mu}{\sigma} \) - Where X is the value we are interested in (46 years), μ is the mean (52.8 years), and σ is the standard deviation (10.3 years). 3. **Look up the Z-Score in a Standard Normal Distribution Table:** - The Z-Score will help us find the probability of a value occurring within a normal distribution. 4. **Determine the Correct Probability:** - Finally, use the Z-score to find the probability and correlate it with the given choices. **Graph Interpretation:** To explain this concept, we visualize it using a bell curve. The mean (52.8 years) is at the center, and as we move left or right, the curve illustrates the distribution of ages. The area under the curve up to a certain point corresponds to the probability. By solving this, you will better understand how to use normal distribution and standard deviation to find the probability of a certain range of outcomes. --- For a detailed step-by-step solution, refer to our section on **Normal Distributions and Probability Calculations.**
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