The image you uploaded contains two main formulas used in statistics:

1. Part 1: Calculate $z$ (Z-score):
   The formula is: $z = \frac{X - \mu}{SD}$

   • $X$ is the observed value.
   • $\mu$ is the mean.
   • $SD$ is the standard deviation.

   To calculate the Z-score, you need to plug in the values of $X$, $\mu$, and $SD$ into this formula.

2. Part 2: Find the X-value given a Z-score:
   The formula is: $X = \mu + (z \cdot SD)$

   • $z$ is the given Z-score.
   • $\mu$ is the mean.
   • $SD$ is the standard deviation.

To help you input the correct formulas into the boxes provided:

Part 1:

For calculating $z$:

• The formula for calculating $z$ should be entered as:
  $z = \frac{X - \mu}{SD}$

Part 2:

For calculating $X$ from a given Z-score:

• The formula for calculating $X$ should be entered as:
  $X = \mu + (z \cdot SD)$

Once you input the correct values for $X$, $\mu$, and $SD$, these formulas will give you the result for the Z-score in Part 1 and the X-value in Part 2.

Let me know if you'd like to solve a specific example or need further clarification.

5 Related Questions:

1. How do you interpret the Z-score once it's calculated?
2. What does a high or low Z-score indicate about the data point?
3. How can you use the Z-score to compare data from different distributions?
4. What are the implications if the Z-score is negative?
5. How do you calculate the standard deviation if only raw data is provided?

Tip:

The Z-score represents how many standard deviations a data point is from the mean. This is helpful in comparing data points from different datasets with different means and standard deviations.