Math Problem Statement

Find the area to the right of z = 1.79 under the standard normal curve. (Round to four decimal places as needed.)

Solution

The problem asks for the area to the right of z=1.79z = 1.79 under the standard normal curve. To find this value, follow these steps:

Step 1: Use the Z-table

The Z-table provides the cumulative probability (area) to the left of a given zz-score.

For z=1.79z = 1.79, the cumulative area to the left is approximately 0.9633 based on the Z-table.

Step 2: Find the area to the right

The total area under the standard normal curve is 1. Therefore, the area to the right of z=1.79z = 1.79 is:

Area to the right=1Area to the left\text{Area to the right} = 1 - \text{Area to the left}

Area to the right=10.9633=0.0367\text{Area to the right} = 1 - 0.9633 = 0.0367

Final Answer:

The area to the right of z=1.79z = 1.79 is 0.0367 (rounded to four decimal places).

Would you like a detailed explanation on Z-tables or further assistance?


Related Questions:

  1. What is the area to the left of z=1.79z = -1.79?
  2. How do you calculate areas for two-tailed probabilities in the normal distribution?
  3. What is the probability for 1.5<z<1.5-1.5 < z < 1.5?
  4. How does the shape of the standard normal curve help in probability estimations?
  5. What is the significance of a zz-score in hypothesis testing?

Tip: Always check if you're looking for the left-tail, right-tail, or both when using Z-tables!

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Math Problem Analysis

Mathematical Concepts

Probability
Standard Normal Distribution
Z-Score

Formulas

Area to the right = 1 - Area to the left
Z-Score Table Lookup

Theorems

Standard Normal Distribution
Z-Score Theorem

Suitable Grade Level

Grades 10-12, College