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.