A normal distribution of x-scores is N(38, 4).
Draw the Normal curve and label it.
Convert the x to z-score
Round the z-scores to 2 decimal places.
1) x= 47, z =
2) x= 40, z =
3) x = 38, z =
4) x = 35, z =
5) x = 34, z =
6) x = 25, z =
If the distribution of x-scores is N(38,4) the how do we write the distribution
of z-scores? What are the units for z-scores?


Here are the z-scores corresponding to the given x-scores:

1) \( x = 47 \), \( z = 2.25 \)  
2) \( x = 40 \), \( z = 0.50 \)  
3) \( x = 38 \), \( z = 0.00 \)  
4) \( x = 35 \), \( z = -0.75 \)  
5) \( x = 34 \), \( z = -1.00 \)  
6) \( x = 25 \), \( z = -3.25 \)

### Writing the distribution of z-scores:
The z-scores follow the standard normal distribution, which is written as \( N(0, 1) \), meaning a mean of 0 and a standard deviation of 1.

### Units for z-scores:
Z-scores are unitless, as they represent how many standard deviations a value is from the mean.

Would you like more details on any part of this, or do you have any questions?

Here are five related questions to deepen understanding:
1. How do you interpret a z-score of 2.25?
2. What does it mean when the z-score is 0?
3. How do you calculate probabilities using z-scores?
4. What is the probability of an x-score being greater than 47 in this distribution?
5. How would the normal curve change if the standard deviation were increased?

**Tip:** Z-scores help standardize data, allowing comparison across different normal distributions.

A normal distribution of x-scores is N(38, 4). Draw the Normal curve and label it. Convert the x to z-score. Round the z-scores to 2 decimal places. 1) x = 47, z = ? 2) x = 40, z = ? 3) x = 38, z = ? 4) x = 35, z = ? 5) x = 34, z = ? 6) x = 25, z = ? If the distribution of x-scores is N(38, 4), how do we write the distribution of z-scores? What are the units for z-scores?

This lesson explains how to convert x-scores to z-scores for the normal distribution N(38, 4). It includes step-by-step calculations for six x-scores, rounding z-scores to 2 decimal places. Learn about the properties of the standard normal distribution, including units for z-scores. Suitable for Grades 10-12.

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