The image shows three questions related to calculating z-scores in a normal distribution. Let's solve each:

1. A data value located 1.3 standard deviations below the mean:

• The z-score is simply the number of standard deviations away from the mean, with values below the mean being negative.
• Answer: $z = -1.3$

2. A data value located 2.5 standard deviations above the mean:

• Since the data value is above the mean, the z-score is positive.
• Answer: $z = 2.5$

3. The mean in a normal distribution:

• The mean of a normal distribution corresponds to a z-score of 0 because it is the central value.
• Answer: $z = 0$

Would you like a more detailed explanation of these z-score concepts?

Here are 5 related questions for further exploration:

1. What is the general formula for calculating a z-score?
2. How does the shape of a normal distribution help with understanding z-scores?
3. What percentage of data lies within 1 standard deviation of the mean in a normal distribution?
4. How do z-scores help in comparing values from different distributions?
5. What is the z-score of a data point that is exactly 1 standard deviation below the mean?

Tip: In a normal distribution, approximately 68% of data lies within ±1 standard deviation from the mean.