Find the​ z-score such that the area under the standard normal curve to the left is 0.68.

To find the \( z \)-score such that the area under the standard normal curve to the left of it is 0.68, you can use the standard normal distribution table or a statistical calculator.

Here’s how to do it:

1. The area to the left of the \( z \)-score is given as 0.68.
2. You look up this area in the standard normal distribution table, or use the inverse cumulative distribution function (often denoted as \( \Phi^{-1}(0.68) \)).

Using the standard normal distribution:

- The \( z \)-score that corresponds to an area of 0.68 is approximately **0.47**.

This means that a \( z \)-score of 0.47 corresponds to 68% of the distribution lying to the left of it.

Would you like to know more details or have any questions?

Here are five related questions you might find useful:
1. What is the \( z \)-score corresponding to an area of 0.75 to the left?
2. How do you find the area to the right of a given \( z \)-score?
3. What is the \( z \)-score corresponding to the first quartile (25th percentile) of the standard normal distribution?
4. How would you calculate the area between two \( z \)-scores?
5. How can you find the \( z \)-score if given the area to the right?

**Tip:** When using a standard normal distribution table, remember that the table typically gives the area to the left of the \( z \)-score.

Learn how to find the z-score such that the area under the standard normal curve to the left is 0.68. Use the standard normal distribution table or the inverse cumulative distribution function (\( \Phi^{-1}(0.68) \)) to solve this statistical problem. Understand how the z-score corresponds to specific areas in the standard normal distribution.

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