Math Problem Statement

The total area to the left of zequalsnegative 1.34 and to the right of zequals2.26 under the standard normal curve is

enter your response here. ​(Round to four decimal places as​ needed.)

Solution

To find the total area under the standard normal curve to the left of z=1.34z = -1.34 and to the right of z=2.26z = 2.26, we can use the standard normal distribution table (Z-table) or a calculator.

  1. Area to the left of z=1.34z = -1.34:

    • From the Z-table, the area to the left of z=1.34z = -1.34 is approximately 0.09010.0901.
  2. Area to the right of z=2.26z = 2.26:

    • From the Z-table, the area to the left of z=2.26z = 2.26 is approximately 0.98780.9878.
    • Therefore, the area to the right is 10.9878=0.01221 - 0.9878 = 0.0122.
  3. Total area:

    • The total area to the left of z=1.34z = -1.34 and to the right of z=2.26z = 2.26 is: 0.0901+0.0122=0.10230.0901 + 0.0122 = 0.1023

Thus, the total area is approximately 0.1023 (rounded to four decimal places).

Would you like any further details or explanations? Here are some related questions to consider:

  1. How do you interpret the areas under the normal curve?
  2. What is the significance of the standard normal distribution in statistics?
  3. Can you explain how to use a Z-table effectively?
  4. How do you calculate areas for other values of zz?
  5. What is the relationship between zz-scores and probabilities?

Tip: When calculating areas under the curve, always remember to consider both tails and whether you're looking for areas to the left or right of specific zz-scores.

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Math Problem Analysis

Mathematical Concepts

Statistics
Probability
Standard Normal Distribution
Z-Scores

Formulas

Area under the standard normal curve
1 - P(Z < z) for right-tail probability

Theorems

Properties of the Standard Normal Distribution

Suitable Grade Level

Grades 10-12