Find the X value corresponding to z = 0.75 for each of the following distributions.
µ = 90 and σ = 4	X = 
µ = 90 and σ = 8	X = 
µ = 90 and σ = 12	X = 
µ = 90 and σ = 20	X = 


To find the \( X \) value corresponding to \( z = 0.75 \) for each distribution, we use the following formula:

\[
X = \mu + z \cdot \sigma
\]

Where:
- \( \mu \) is the mean,
- \( \sigma \) is the standard deviation,
- \( z \) is the z-score (which is 0.75 in this case).

### 1. For \( \mu = 90 \) and \( \sigma = 4 \):
\[
X = 90 + (0.75 \cdot 4) = 90 + 3 = 93
\]

### 2. For \( \mu = 90 \) and \( \sigma = 8 \):
\[
X = 90 + (0.75 \cdot 8) = 90 + 6 = 96
\]

### 3. For \( \mu = 90 \) and \( \sigma = 12 \):
\[
X = 90 + (0.75 \cdot 12) = 90 + 9 = 99
\]

### 4. For \( \mu = 90 \) and \( \sigma = 20 \):
\[
X = 90 + (0.75 \cdot 20) = 90 + 15 = 105
\]

### Summary of \( X \)-values:
1. \( \mu = 90 \), \( \sigma = 4 \): \( X = 93 \)
2. \( \mu = 90 \), \( \sigma = 8 \): \( X = 96 \)
3. \( \mu = 90 \), \( \sigma = 12 \): \( X = 99 \)
4. \( \mu = 90 \), \( \sigma = 20 \): \( X = 105 \)

Would you like further explanation or details on this?

Here are 5 related questions to consider:
1. How would the value of \( X \) change if \( z \) was negative?
2. What is the interpretation of a z-score in a normal distribution?
3. Can you calculate the \( X \)-value if \( z \) is 1.25 for \( \mu = 90 \) and \( \sigma = 12 \)?
4. What is the significance of the standard deviation in a normal distribution?
5. How would you find \( z \)-values for a given \( X \)?

**Tip:** The z-score tells you how many standard deviations a data point is from the mean.

Find the X value corresponding to z = 0.75 for each of the following distributions.
µ = 90 and σ = 4 X =
µ = 90 and σ = 8 X =
µ = 90 and σ = 12 X =
µ = 90 and σ = 20 X =

Learn how to find the X value corresponding to a z-score of 0.75 for different normal distributions where µ = 90 and σ = 4, 8, 12, and 20. This solution covers key statistical concepts like z-scores and the normal distribution formula. Suitable for students in Grades 9-12.

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