To find the probability of Z being greater than 1.25 in the standard normal distribution, we first need to understand what the standard normal distribution is. The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. The Z-scores indicate how many standard deviations an element is from the mean.
1. **Finding the Z-Score:**
In this case, you are looking for P(Z > 1.25). The Z-score of 1.25 tells us how far from the mean we are interested in (1.25 standard deviations above the mean).
2. **Using Z-Table or Calculator:**
To find the probability, we typically use a Z-table, which provides the area (probability) to the left of a given Z score. From the Z-table, we find the value corresponding to Z = 1.25. This value is approximately 0.8944. This means that about 89.44% of the data in the standard normal distribution falls below a Z-score of 1.25.
3. **Calculating the Probability:**
Since we want the probability of Z being greater than 1.25, we need the area to the right. We can calculate this by subtracting the value we found from 1:
P(Z > 1.25) = 1 – P(Z < 1.25)
P(Z > 1.25) = 1 – 0.8944 = 0.1056
4. **Conclusion:**
Therefore, the probability of a Z score being greater than 1.25 is approximately 0.1056, or 10.56%. This means that about 10.56% of the data points in a standard normal distribution fall above a Z-score of 1.25.