### Finding the Z-Score for a Given Distribution AreaTo find the z-score for which 80% of the distribution's area lies to its right, follow the options provided and understand the context of z-scores in a normal distribution.#### Question:**Find the z-score for which 80% of the distribution's area lies to its right.**#### Answer Choices:- **-1.84**- **-2.16**- **-0.84**- **-0.52**#### Explanation:In a standard normal distribution, the z-score represents the number of standard deviations away from the mean. The area to the right of a z-score translates to the probability that a value will fall above that z-score. For 80% of the distribution's area to lie to the right, we must look for a z-score corresponding to a cumulative area of 20% (since 100% - 80% = 20%) to the left. This can be found using z-tables or statistical software.Statistical tables or software might be used to precisely determine that the z-score is approximately -0.84 (meaning a z-score of -0.84 accumulates 0.20 or 20% on its left-hand side).Therefore, the correct answer is:- **-0.84**#### Graph Explanation:No graph is provided in the question, but a typical graph for this problem would include a bell-shaped normal distribution curve. The curve should be divided such that 20% of the area lies to the left of the specific z-score and 80% to the right.For educational websites, it's crucial to illustrate such a scenario using a labeled normal distribution curve, highlighting the exact sections and providing comprehensive steps to use z-tables or software tools.For further understanding, practice finding cumulative areas and corresponding z-scores using standard normal distribution tables available in most statistical textbooks or online resources.

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Statistics

Find the z-score for which 80% of the distribution's area lies to its right.

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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Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.

Question

### Finding the Z-Score for a Given Distribution Area

To find the z-score for which 80% of the distribution's area lies to its right, follow the options provided and understand the context of z-scores in a normal distribution.

#### Question:
**Find the z-score for which 80% of the distribution's area lies to its right.**

#### Answer Choices:

- **-1.84**
- **-2.16**
- **-0.84**
- **-0.52**

#### Explanation:
In a standard normal distribution, the z-score represents the number of standard deviations away from the mean. The area to the right of a z-score translates to the probability that a value will fall above that z-score.

For 80% of the distribution's area to lie to the right, we must look for a z-score corresponding to a cumulative area of 20% (since 100% - 80% = 20%) to the left. This can be found using z-tables or statistical software.

Statistical tables or software might be used to precisely determine that the z-score is approximately -0.84 (meaning a z-score of -0.84 accumulates 0.20 or 20% on its left-hand side).

Therefore, the correct answer is:
- **-0.84**

#### Graph Explanation:
No graph is provided in the question, but a typical graph for this problem would include a bell-shaped normal distribution curve. The curve should be divided such that 20% of the area lies to the left of the specific z-score and 80% to the right.

For educational websites, it's crucial to illustrate such a scenario using a labeled normal distribution curve, highlighting the exact sections and providing comprehensive steps to use z-tables or software tools.

For further understanding, practice finding cumulative areas and corresponding z-scores using standard normal distribution tables available in most statistical textbooks or online resources.

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