A certain value has a standardized score $$ =1.75 $$. How many standard deviations from the mean does this value fall?

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A standardized score, or z-score, indicates how many standard deviations a particular value is from the mean of a distribution. The formula for calculating a z-score is:

$$
z = \frac{{x - \mu}}{{\sigma}}
$$

Where:
- $$ z $$ is the standardized score,
- $$ x $$ is the value,
- $$ \mu $$ is the mean,
- $$ \sigma $$ is the standard deviation.

In your case, the standardized score is $$ z = 1.75 $$. This means that the value $$ x $$ is **1.75 standard deviations above the mean**.

**Interpretation:**
- **Positive z-score (e.g., 1.75):** The value is above the mean.
- **Negative z-score:** The value is below the mean.
- **Z-score of 0:** The value is exactly at the mean.

So, a z-score of 1.75 indicates that the value is 1.75 standard deviations **above** the mean.

**Example:**
If the mean height of a group is 170 cm with a standard deviation of 10 cm, a person with a height corresponding to a z-score of 1.75 would be:

$$
x = \mu + z \times \sigma = 170 \, \text{cm} + 1.75 \times 10 \, \text{cm} = 187.5 \, \text{cm}
$$

This person is 1.75 standard deviations taller than the average height in the group.

**Summary:**  
A standardized score of 1.75 means the value is 1.75 standard deviations above the mean.
A standardized score of 1.75 means the value is 1.75 standard deviations above the mean.

A certain value has a standardized score . How many standard deviations from the mean does this value fall?

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