Math Problem Statement

For a standard normal distribution, find:

P(z < 1.79)

Solution

To find P(z<1.79)P(z < 1.79) for a standard normal distribution, we look up the z-score of z=1.79z = 1.79 in the standard normal distribution table, or we can use statistical software or a calculator.

For a standard normal distribution:

  1. Locate z=1.7z = 1.7 in the row and 0.090.09 in the column (since 1.79 = 1.7 + 0.09).
  2. This value corresponds to the probability that zz is less than 1.79.

Using the standard normal table, we find:

P(z<1.79)0.9633P(z < 1.79) \approx 0.9633

Thus,

P(z<1.79)0.9633P(z < 1.79) \approx 0.9633

Would you like further details or have questions about this?

Here are some related questions you might find interesting:

  1. What is the probability P(z>1.79)P(z > 1.79) for the standard normal distribution?
  2. How would you find P(z<1.79)P(z < -1.79) in a standard normal distribution?
  3. What is the probability P(z<0)P(z < 0) for a standard normal distribution?
  4. How can we use symmetry properties of the normal distribution for these calculations?
  5. What is the cumulative probability for P(1.79<z<1.79)P(-1.79 < z < 1.79)?

Tip: For the standard normal distribution, you can use tables or software to find cumulative probabilities directly.

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Math Problem Analysis

Mathematical Concepts

Statistics
Probability
Standard Normal Distribution

Formulas

P(z < a) for z-scores
Using z-tables for cumulative probability

Theorems

Properties of the standard normal distribution

Suitable Grade Level

Grades 10-12