Math Problem Statement

Find the percent of the total area under the standard normal curve between the z-scores of z = 0.75 and z = 1.6.

Solution

To find the percent of the total area under the standard normal curve between the z-scores of z=0.75z = 0.75 and z=1.6z = 1.6, we can use the values from the standard normal table you provided.

  1. Locate z=0.75z = 0.75:

    • From the table, the area to the left of z=0.75z = 0.75 is approximately 0.773.
  2. Locate z=1.6z = 1.6:

    • From the table, the area to the left of z=1.6z = 1.6 is approximately 0.945.
  3. Calculate the area between z=0.75z = 0.75 and z=1.6z = 1.6:

    • Subtract the area at z=0.75z = 0.75 from the area at z=1.6z = 1.6: 0.9450.773=0.1720.945 - 0.773 = 0.172

So, the percent of the area under the curve between z=0.75z = 0.75 and z=1.6z = 1.6 is 17.2%.

Would you like further details or have any questions?

Related Questions

  1. What is the area under the curve between z=0.5z = 0.5 and z=1.5z = 1.5?
  2. How do you find the area to the right of a specific z-score?
  3. What does it mean if a z-score has an area of 0.5?
  4. Can we find the area under the curve between negative and positive z-scores, such as between z=1z = -1 and z=1z = 1?
  5. How does the standard normal table relate to percentiles in statistics?

Tip: Always check if you are finding the area between two z-scores by subtracting the smaller area from the larger.

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Math Problem Analysis

Mathematical Concepts

Statistics
Probability
Standard Normal Distribution

Formulas

Area under the curve between two z-scores = Area(z2) - Area(z1)

Theorems

Properties of the Standard Normal Distribution

Suitable Grade Level

Grades 10-12