# How To Find The Z Score Given The Confidence Level of a Normal Distribution 2

TLDRThis educational video introduces a quick and simple method for finding z-scores based on given confidence levels. It starts by presenting common z-values for confidence levels of 90%, 95%, 98%, and 99%. The video explains how to calculate the area under the curve to the left of the z-score by adjusting the confidence level to a decimal and applying a formula. Through visual illustrations and a step-by-step guide, viewers learn to use a z-score table to find the exact z-score corresponding to specific confidence levels. The video further challenges viewers with practice problems for confidence levels of 97% and 92%, demonstrating the process of calculating the area to the left and using the z-score table to find the corresponding z-scores. This instructional video makes understanding and applying statistical concepts accessible, emphasizing practical skills in statistical analysis.

###### Takeaways

- ๐ Common Z-score values for confidence levels: 90% = 1.645, 95% = 1.96, 98% = 2.33, 99% = 2.575.
- ๐ฎ To find a Z-score from a confidence level, calculate the area under the curve to the left using the formula: (1 + confidence level) / 2.
- ๐ Confidence level percentages must be converted to decimal form (e.g., 95% becomes 0.95) for calculations.
- ๐ The area under the curve between the negative and positive Z-scores represents the confidence level.
- ๐ฌ For a 95% confidence level, the area to the left of the positive Z-score is calculated as 0.975 (0.95 + 0.025).
- ๐ Z-scores can be identified using a positive Z-score table by matching the calculated area to the left.
- ๐ซ Practice task: Determine Z-scores for confidence levels of 97% and 92%.
- ๐ฌ For a 97% confidence level, the area to the left is 0.985; for a 92% confidence level, it's 0.96.
- ๐ Z-score examples: 97% confidence level corresponds to a Z-score of 2.17, and 92% corresponds to 1.75.
- ๐ The Z-score table helps convert a confidence level into an area, which can then be used to find the corresponding Z-score.

###### Q & A

### What is a z-score and how is it used in statistics?

-A z-score represents how many standard deviations a data point is from the mean. It allows you to compare data from different normal distributions on the same scale. Z-scores are useful in hypothesis testing and calculating confidence intervals.

### What formula can we use to calculate the area under the normal curve to the left of a z-score?

-The area under the normal curve to the left of a z-score can be calculated using: Area = 1 + (Confidence Level / 100) / 2

### If we have a 95% confidence level, what is the corresponding z-score?

-For a 95% confidence level, the z-score is 1.96. This can be calculated by finding the area under the curve using the formula, which is 0.975. Then looking up 0.975 in the z-score table to find the z-score of 1.96.

### How do we use a z-score table to find the z-score for a given area under the curve?

-First locate the area value in the z-score table. Then identify the row and column the area value corresponds to. Add the row and column values together to get the z-score.

### What are some common confidence levels and their associated z-scores?

-Some common confidence levels and z-scores are: 90% confidence level - z-score of 1.645, 95% confidence level - z-score of 1.96, 98% confidence level - z-score of 2.33, 99% confidence level - z-score of 2.575.

### Why do we need to find the area under the curve to determine the z-score?

-The area under the normal curve corresponds to probability. By finding the area, we can identify the portion of the distribution that falls within a certain number of standard deviations from the mean, which allows us to determine the z-score.

### What is the purpose of using z-scores and confidence levels in statistics?

-Z-scores and confidence levels allow us to quantify certainty. They are used in hypothesis testing to determine if a result is statistically significant and in constructing confidence intervals to estimate population parameters.

### How can you calculate a z-score if you don't have access to a z-score table?

-You can use statistical software or a calculator that has the inverse normal distribution function. This allows you to input the area under the curve and it will output the corresponding z-score.

### What are some examples of when you would need to find a z-score in real-world applications?

-Some examples are: determining credit risk scores, evaluating investment performance, analyzing survey results, setting manufacturing quality control limits, and assessing medical test results.

### What should you do if the area under the curve you calculate does not exist in the z-score table?

-If the area is not in the table, you can interpolate between the closest values. For example, if your area is 0.987, estimate between the 0.985 and 0.990 rows.

###### Outlines

##### ๐ Finding the z-score from a confidence level

This paragraph explains how to calculate the z-score corresponding to a given confidence level. It provides the formula to compute the area under the curve and gives examples of common confidence levels like 90%, 95%, etc. and their corresponding z-scores. It also demonstrates how to use the z-score table to look up the z-score for a calculated area.

##### ๐ Practice problems on finding z-scores

This paragraph provides two practice problems to find the z-scores for confidence levels of 97% and 92%. It walks through calculating the area under the curve using the formula for each confidence level. Then it shows how to look up those area values in the z-score table to identify the matching z-scores of 2.17 and 1.75.

###### Mindmap

###### Keywords

##### ๐กz-score

##### ๐กconfidence level

##### ๐กarea under the curve

##### ๐กmean

##### ๐กstandard deviation

##### ๐กnormal distribution

##### ๐กz-table

##### ๐กconfidence interval

##### ๐กp-value

##### ๐กhypothesis testing

###### Highlights

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###### Transcripts

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