Math Problem Statement

For the standard normal distribution shown on the​ right, find the probability of z occurring in the indicated region.Click here to view page 1 of the standard normal table.-0.91A normal curve is over a horizontal axis. A vertical line segment extends from the horizontal axis to the curve at negative 0.91. The area under the curve and to the left of the vertical line segment is shaded.Question content area bottomPart 1The probability is enter your response here.

Solution

To solve this problem, we need to find the cumulative probability for z=0.91z = -0.91 under the standard normal distribution curve. This is the area under the curve to the left of z=0.91z = -0.91.

Steps:

  1. Use the Standard Normal Table to look up the cumulative probability for z=0.91z = -0.91.
  2. Locate the row corresponding to z=0.9z = -0.9 and the column for 0.010.01. The intersection gives the cumulative probability.

From the standard normal table:

P(Z0.91)=0.1814P(Z \leq -0.91) = 0.1814

Final Answer:

The probability is 0.1814.


Would you like to see an explanation of how the standard normal table works, or any further calculations?

Here are 5 related questions for deeper understanding:

  1. What is the probability of zz being greater than 0.91-0.91?
  2. How do we find the probability for zz values greater than or equal to a given point?
  3. What is the symmetry property of the standard normal distribution?
  4. How is the z-score related to real-world applications like confidence intervals?
  5. Can we calculate probabilities for non-standard normal distributions?

Tip: Always use the symmetry

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Math Problem Analysis

Mathematical Concepts

Probability
Standard Normal Distribution
Cumulative Probability

Formulas

P(Z ≤ z) = Area under the standard normal curve to the left of z

Theorems

Properties of the Standard Normal Distribution

Suitable Grade Level

Grades 9-12