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To solve for the z-score, we will use the formula:

\[
z = \frac{X - \mu}{\sigma}
\]

where:
- \(X\) is the value,
- \(\mu\) is the mean,
- \(\sigma\) is the standard deviation.

Now, let's go step by step for each question:

### 1. Given \(X = 55\), \(s = 5\), and \(\mu = 60\):
Using the formula:
\[
z = \frac{55 - 60}{5} = \frac{-5}{5} = -1
\]
The z-score for this case is \(z = -1\).

### 2. Given \(X = 75\), \(\sigma = 10\), and \(\mu = 55\):
Using the formula:
\[
z = \frac{75 - 55}{10} = \frac{20}{10} = 2
\]
The z-score for this case is \(z = 2\).

### 3. Given \(X = 100\), \(\sigma = 4\), and \(\mu = 135\):
Using the formula:
\[
z = \frac{100 - 135}{4} = \frac{-35}{4} = -8.75
\]
The z-score for this case is \(z = -8.75\).

Let me know if you need any further clarification or detailed explanation! Also, here are some related questions for you:

1. How do z-scores help in interpreting data?
2. Can the z-score be negative or greater than 3? What does that indicate?
3. How do you calculate the z-score when the standard deviation is given as a sample standard deviation instead of the population standard deviation?
4. What is the interpretation of a z-score of 0?
5. How do z-scores relate to probability in a normal distribution?

Tip: Z-scores are particularly useful in understanding how far away a particular data point is from the mean, which is important in various statistical analyses such as hypothesis testing.

Solve the following z-score using the formula. Show your complete solutions. 1. X = 55, s = 5, μ = 60 2. X = 75, σ = 10, μ = 55 3. X = 100, σ = 4, μ = 135

Learn how to calculate z-scores for statistical problems using the formula z = (X - μ) / σ. Includes complete step-by-step solutions for the given values: X = 55, s = 5, μ = 60; X = 75, σ = 10, μ = 55; and X = 100, σ = 4, μ = 135. Perfect for high school students in Grades 10-12.

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