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Suppose the age that children learn to walk is normally distributed with mean 12 months and standard deviation 1.5 month. 15 randomly selected people were asked what age they learned to walk. Round all answers to 4 decimal places where possible. a. What is the probability that one randomly selected person learned to walk when the person was between 11.5 and 12.5 months old? 2586 b. For the 15 people, find the probability that the average age that they learned to walk is between 11.5 and 12.5 months old. 8030 c. For part b, is the assumption that the distribution is normal necessary? D YesO Na a d. Find the IQR for the average first time walking age for groups of 15 people. Round to two decimal places. Q1 = months 03 = months

Suppose the age that children learn to walk is normally distributed with mean 12 months and standard deviation 1.5 month. 15 randomly selected people were asked what age they learned to walk. Round all answers to 4 decimal places where possible. a. What is the probability that one randomly selected person learned to walk when the person was between 11.5 and 12.5 months old? 2586 b. For the 15 people, find the probability that the average age that they learned to walk is between 11.5 and 12.5 months old. 8030 c. For part b, is the assumption that the distribution is normal necessary? D YesO Na a d. Find the IQR for the average first time walking age for groups of 15 people. Round to two decimal places. Q1 = months 03 = months

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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**Understanding Statistical Probability in Early Walking Ages** **Overview:** This study examines the ages at which children typically learn to walk. The ages are assumed to follow a normal distribution with a mean of 12 months and a standard deviation of 1.5 months. A sample of 15 individuals was surveyed to determine the age they learned to walk. The answers to the questions below are rounded to four decimal places where applicable. **Details:** - **Question a:** Determine the probability that a randomly selected child learned to walk between the ages of 11.5 and 12.5 months. The calculated probability is **0.2588**, though the assessment indicates that this value might be incorrect. - **Question b:** Evaluate the probability that the average walking age for the 15 surveyed individuals falls between 11.5 and 12.5 months. The probability is **0.8030**, which is confirmed to be correct. - **Question c:** Assess whether assuming a normal distribution is necessary for calculating the probability in part b. The assessment confirms that a normal distribution assumption is indeed necessary, as indicated by the selection of "Yes." - **Question d:** Find the Interquartile Range (IQR) for the average first walking age for groups of 15 people. This requires calculations for: - \( **Q1** = \) _____ months - \( **Q3** = \) _____ months - \( **IQR** = \) _____ months The values are left blank, indicating that further calculation is needed. This analysis leverages statistical methods to understand variations in early walking development, with normal distribution parameters providing a framework for interpreting individual and group data. Further exploration is required for full completion, particularly in calculating precise IQR values.
Transcribed Image Text:**Understanding Statistical Probability in Early Walking Ages** **Overview:** This study examines the ages at which children typically learn to walk. The ages are assumed to follow a normal distribution with a mean of 12 months and a standard deviation of 1.5 months. A sample of 15 individuals was surveyed to determine the age they learned to walk. The answers to the questions below are rounded to four decimal places where applicable. **Details:** - **Question a:** Determine the probability that a randomly selected child learned to walk between the ages of 11.5 and 12.5 months. The calculated probability is **0.2588**, though the assessment indicates that this value might be incorrect. - **Question b:** Evaluate the probability that the average walking age for the 15 surveyed individuals falls between 11.5 and 12.5 months. The probability is **0.8030**, which is confirmed to be correct. - **Question c:** Assess whether assuming a normal distribution is necessary for calculating the probability in part b. The assessment confirms that a normal distribution assumption is indeed necessary, as indicated by the selection of "Yes." - **Question d:** Find the Interquartile Range (IQR) for the average first walking age for groups of 15 people. This requires calculations for: - \( **Q1** = \) _____ months - \( **Q3** = \) _____ months - \( **IQR** = \) _____ months The values are left blank, indicating that further calculation is needed. This analysis leverages statistical methods to understand variations in early walking development, with normal distribution parameters providing a framework for interpreting individual and group data. Further exploration is required for full completion, particularly in calculating precise IQR values.
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