Math Problem Statement

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

zless than or equals≤negative 1.94−1.94

Solution

To find the percentage of values in a normal distribution that are less than or equal to z=1.94z = -1.94, you can follow the same procedure as before.

Result:

Looking up z=1.94z = -1.94 in the Z-table, the cumulative probability corresponding to this z-score is approximately 0.0262.

Interpretation:

This means that approximately 2.62% of the values in a normal distribution are less than or equal to z=1.94z = -1.94.

Would you like to explore this concept further or have any additional questions?

Here are some related questions you might find helpful:

  1. How does the area under the curve relate to z-scores?
  2. What is the z-score for a certain percentile in a normal distribution?
  3. How can you calculate the probability between two z-scores?
  4. What is the relationship between z-scores and standard deviations?
  5. How do you interpret a z-score in terms of standard deviations from the mean?

Tip: Always remember that the Z-table gives you the cumulative probability from the far left up to the specified z-score. For z-scores below zero, this represents the percentage of values that are less than or equal to that z-score in the distribution.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Statistics
Normal Distribution

Formulas

Z-score formula
Cumulative Probability formula

Theorems

Central Limit Theorem

Suitable Grade Level

High School