5. Reach Distance. The overhead reach distances of adult women are normally distributed with a mean of 200 cm. and a standard deviation of 12.5 cm. (Illustrate each with a graph!) a. Find the probability that an individual distance is greater than 205 cm. Describe the random variable: Describe distribution: b. Find the probability that the mean reach distance for 25 randomly selected adult women is greater than 205 cm. Describe the random variable: Is it appropriate for us to use The Central Limit Theorem? Describe the distribution:

5. Reach Distance. The overhead reach distances of adult women are normally distributed with a mean of 200 cm. and a standard deviation of 12.5 cm. (Illustrate each with a graph!) a. Find the probability that an individual distance is greater than 205 cm. Describe the random variable: Describe distribution: b. Find the probability that the mean reach distance for 25 randomly selected adult women is greater than 205 cm. Describe the random variable: Is it appropriate for us to use The Central Limit Theorem? Describe the distribution:

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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A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

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**5. Reach Distance.**

The overhead reach distances of adult women are normally distributed with a mean of 200 cm and a standard deviation of 12.5 cm. (*Illustrate each with a graph!*)

**a.** Find the probability that an individual distance is greater than 205 cm.
Describe the random variable: __________________________
Describe distribution: __________________________

**b.** Find the probability that the mean reach distance for 25 randomly selected adult women is greater than 205 cm.
Describe the random variable: __________________________
Is it appropriate for us to use The Central Limit Theorem? _______________
Describe the distribution: __________________________

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This problem involves understanding the concepts of normal distribution and the Central Limit Theorem. For part (a), you must calculate the probability for a single observation, while part (b) requires understanding how the sample mean's distribution is affected by sample size. Ensure to include graphs that illustrate the normal distribution and sample distribution for clarification.

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