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Part 1
Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.

z0.1711
0

A symmetric bell-shaped curve is plotted over a horizontal scale with two labeled coordinates. One coordinate is labeled "0" and is located at the center and peak of the curve. The other coordinate is labeled "z," and is to the right of 0. A vertical line extends from the scale to the curve at z. The area under the curve to the right of z is shaded and labeled “0.1711.”
Question content area bottom
Part 1
The indicated z score is

​(Round to two decimal places as​ needed.)

To find the indicated z score for which the area to the right of the z score is 0.1711, you can use the standard normal distribution table or a calculator with statistical functions.

Given:
- Mean (μ) = 0
- Standard deviation (σ) = 1
- Area to the right of \( z \) (P(Z > z)) = 0.1711

We need to find the z score such that \( P(Z > z) = 0.1711 \).

1. The area to the left of \( z \) is \( 1 - 0.1711 = 0.8289 \).

Now, look up the cumulative probability (0.8289) in the standard normal distribution table or use a calculator to find the corresponding z score.

Using the standard normal distribution table:
- Find the value closest to 0.8289 in the table.
- The corresponding z score is approximately 0.95.

Thus, the z score corresponding to an area of 0.1711 to the right is \( z = 0.95 \).

**The indicated z score is 0.95.**

Do you want details or have any questions?

Here are 5 more questions you might want to ask:
1. How do you find a z score given a specific probability?
2. What are the properties of the standard normal distribution?
3. How can you use z scores to compare different data sets?
4. What is the relationship between z scores and percentiles?
5. How do you calculate probabilities using z scores?

**Tip:** When using standard normal distribution tables, ensure you understand whether the table provides cumulative probabilities from the left or right to avoid confusion in finding the correct z score.

Learn how to find the indicated z score in a standard normal distribution with mean 0 and standard deviation 1. Understand the process of using cumulative probabilities and standard normal distribution tables. Suitable for undergraduate students studying statistics and probability.

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