Find the percentage of all values in a normal distribution for the following​ z-score.

zless than or equals≤negative 1.86−1.86

To find the percentage of values in a normal distribution that are less than or equal to \( z = -1.86 \), you can use the standard normal distribution table (also known as the Z-table) or a calculator that provides cumulative probabilities for the standard normal distribution.

1. **Using the Z-table**: Look up the value of \( z = -1.86 \) in the Z-table. The Z-table gives you the cumulative probability from the far left up to that z-score.

2. **Using a calculator or software**: You can also directly find the cumulative probability for \( z = -1.86 \) using a statistical calculator or software.

### Result:
Looking up \( z = -1.86 \) in the Z-table, you find the cumulative probability corresponding to this z-score is approximately **0.0314**.

### Interpretation:
This means that approximately **3.14%** of the values in a normal distribution are less than or equal to \( z = -1.86 \).

Would you like more details on how to use the Z-table or have any further questions?

Here are some related questions you might find helpful:
1. How do you interpret a Z-score in a normal distribution?
2. What percentage of values lies between two z-scores?
3. How can you calculate the probability for a positive z-score?
4. What is the probability for a z-score greater than a given value?
5. How do you standardize a raw score to find its z-score?

**Tip:** The Z-table is a valuable tool for quickly finding cumulative probabilities, but understanding how to use it properly is key to interpreting normal distributions effectively.

Learn how to find the percentage of values in a normal distribution that are less than or equal to z = -1.86. Use the Z-table or a calculator to determine the cumulative probability for this specific z-score. Interpret the result to understand the proportion of values below -1.86 in a standard normal distribution.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation