To determine the approximate value of [tex]\( P(z \geq -1.25) \)[/tex] for a standard normal distribution, follow these steps:
### Step-by-Step Solution:
1. Recognize the Symmetry of the Standard Normal Distribution:
The standard normal distribution (or Z-distribution) is symmetric around [tex]\( z = 0 \)[/tex]. This symmetry means [tex]\( P(z \geq -1.25) \)[/tex] is equal to [tex]\( P(z \leq 1.25) \)[/tex].
2. Using the Standard Normal Table:
The standard normal table (or Z-table) typically provides the cumulative probability from the left up to the given z-value. From the provided table:
- For [tex]\( z = 1.25 \)[/tex]: The cumulative probability [tex]\( P(z \leq 1.25) = 0.8944 \)[/tex].
3. Interpret the Table Value for Our Desired Probability:
Since [tex]\( P(z \geq -1.25) = P(z \leq 1.25) \)[/tex]:
Therefore, [tex]\( P(z \geq -1.25) = 0.8944 \)[/tex].
4. Convert the Probability to a Percentage:
To convert the probability to a percentage:
- [tex]\( 0.8944 \times 100 = 89.44\% \)[/tex].
### Conclusion:
The approximate value of [tex]\( P(z \geq -1.25) \)[/tex] for a standard normal distribution, using the given standard normal table, is approximately [tex]\( 89\% \)[/tex].
So, the correct answer from the provided choices is [tex]\( 89\% \)[/tex].
