Use the accompanying table of​ z-scores and percentiles to find the percentage of data items in a normal distribution that lie a. below and b. above a​ z-score of 0.45.
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Part 1
a. The percentage of data items that lie below the​ z-score is 
  
enter your response here​%.
​(Round to two decimal places as​ needed.)


To find the percentage of data items that lie below a z-score of 0.45 in a normal distribution, we can use a **z-score table** (also known as a standard normal distribution table).

Here’s the step-by-step process:

1. **Locate the z-score** of **0.45** on the z-score table. Most tables provide the area under the curve to the left of the given z-score (which represents the percentage of data items below the z-score).
   
2. According to the z-score table, the area corresponding to **z = 0.45** is approximately **0.6736**.

3. To convert this to a percentage, multiply by 100:  
   \[
   0.6736 \times 100 = 67.36\%
   \]

So, the percentage of data items that lie below the z-score of **0.45** is **67.36%**.

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### Part 2: Percentage of Data Items Above the Z-Score

To find the percentage of data items above the z-score of 0.45:

1. Subtract the percentage below from 100%:  
   \[
   100\% - 67.36\% = 32.64\%
   \]

Thus, **32.64%** of data items lie above a z-score of **0.45**.

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Would you like more details or clarification on any part of this solution?

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Here are 5 related questions for further practice:

1. What is the percentage of data items below a z-score of -1.25?
2. How do you interpret a z-score of 0 in terms of percentiles?
3. What percentage of data lies between z-scores of -0.75 and 1.25?
4. What is the area under the normal curve between z = 0.45 and z = 1.5?
5. How do you calculate the percentile rank for a z-score of 1.2?

**Tip:** The total area under a normal distribution curve is always 1 (or 100%), which can help when calculating areas above or below certain z-scores.

Use the accompanying table of​ z-scores and percentiles to find the percentage of data items in a normal distribution that lie a. below and b. above a​ z-score of 0.45.

Learn how to find the percentage of data items below and above a z-score of 0.45 in a normal distribution. This problem involves using z-scores, percentiles, and the properties of the standard normal distribution. Suitable for students in Grades 9-12, with step-by-step solutions.

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