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For a standard normal distribution, find the approximate value of [tex]\( P(z \geq -1.25) \)[/tex]. Use the portion of the standard normal table below to help answer the question.

\begin{tabular}{|c|c|}
\hline
[tex]$z$[/tex] & Probability \\
\hline
0.00 & 0.5000 \\
\hline
0.25 & 0.5987 \\
\hline
1.00 & 0.8413 \\
\hline
1.25 & 0.8944 \\
\hline
1.50 & 0.9332 \\
\hline
1.75 & 0.9599 \\
\hline
\end{tabular}

A. 11%
B. 39%
C. 61%
D. 89%



Answer :

GinnyAnswer
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].

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