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To convert the given value (48) to a z-score, we can use the z-score formula:

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

Where:
- \(x = 48\) (the value we are converting),
- \(\mu = 40\) (the mean),
- \(\sigma = 4\) (the standard deviation).

Now, let's substitute the values into the formula:

\[
z = \frac{48 - 40}{4} = \frac{8}{4} = 2
\]

Thus, the z-score for 48 is **2**.

Would you like further details or have any questions?

Here are 5 related questions:
1. What does a z-score of 2 signify in a normal distribution?
2. How would you interpret a negative z-score?
3. How can z-scores be used to compare data from different distributions?
4. What percentage of data falls above a z-score of 2 in a standard normal distribution?
5. How would the z-score change if the standard deviation increased to 5?

**Tip:** Z-scores help determine how far a value is from the mean in terms of standard deviations. A z-score of 2 means the value is 2 standard deviations above the mean.

A set of data items is normally distributed with a mean of 40 and a standard deviation of 4. Convert 48 to a z-score.

Learn how to convert the value 48 to a z-score in a normally distributed dataset with a mean of 40 and standard deviation of 4. This detailed solution covers key statistical concepts and the formula for calculating z-scores. Suitable for students in Grades 10-12.

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