**Problem Statement:**A normal distribution has a mean of 58.4 and a standard deviation of 4.45. Find the data value corresponding to $ z = -3.82 $.The data value is $\_$.(Round to the nearest tenth as needed.)**Instructions:**Enter your answer in the answer box provided. **Explanation:**To find the data value corresponding to a given z-score, use the formula:\[ X = \mu + z \cdot \sigma \]where:- $ X $ is the data value,- $ \mu $ is the mean (58.4 in this case),- $ z $ is the z-score (-3.82),- $ \sigma $ is the standard deviation (4.45).Substitute the values into the formula to solve for $ X $, and then round your answer to the nearest tenth.

Mean = 58.4 Standard deviation = 4.45 Z score = -3.82

Answered: A normal distribution has mean 58.4 and…

A normal distribution has mean 58.4 and standard deviation 4.45. Find the data value corresponding to z= -3.82. The data value is (Round to the nearest tenth as needed)

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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Estimation

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.

Question

**Problem Statement:**

A normal distribution has a mean of 58.4 and a standard deviation of 4.45. Find the data value corresponding to $ z = -3.82 $.

The data value is $\_$.

(Round to the nearest tenth as needed.)

**Instructions:**

Enter your answer in the answer box provided.

**Explanation:**

To find the data value corresponding to a given z-score, use the formula:

\[ X = \mu + z \cdot \sigma \]

where:
- $ X $ is the data value,
- $ \mu $ is the mean (58.4 in this case),
- $ z $ is the z-score (-3.82),
- $ \sigma $ is the standard deviation (4.45).

Substitute the values into the formula to solve for $ X $, and then round your answer to the nearest tenth.

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