Question

For a standard normal distribution, find the approximate value of P (z greater-than-or-equal-to negative 1.25). Use the portion of the standard normal table below to help answer the question.

z
Probability
0.00
0.5000
0.25
0.5987
1.00
0.8413
1.25
0.8944
1.50
0.9332
1.75
0.9599
11%
39%
61%
89%

Answer 1

To find the probability \( P(Z \geq -1.25) \) for a standard normal distribution, we can utilize the symmetry of the normal distribution as well as the values from the standard normal table.

1. The standard normal table typically gives probabilities for \( P(Z \leq z) \), where \( z \) is the z-score.
2. Since the distribution is symmetric, we can find \( P(Z \geq -1.25) \) by calculating it as follows:
\[
P(Z \geq -1.25) = 1 - P(Z < -1.25)
\]

3. We first need to determine \( P(Z < -1.25) \). The standard normal table usually provides \( P(Z < z) \) for positive values of \( z \). Thus, we can find \( P(Z < -1.25) \) by finding \( P(Z < 1.25) \) and then using the fact that \( P(Z < -z) = 1 - P(Z < z) \).

4. From the standard normal table in your question, we see that:
- \( P(Z < 1.25) = 0.8944 \)

5. Thus, we can find \( P(Z < -1.25) \):
\[
P(Z < -1.25) = 1 - P(Z < 1.25) = 1 - 0.8944 = 0.1056
\]

6. Now we can find \( P(Z \geq -1.25) \):
\[
P(Z \geq -1.25) = 1 - P(Z < -1.25) = 1 - 0.1056 = 0.8944
\]

Thus, the approximate value of \( P(Z \geq -1.25) \) is approximately **0.8944**.