Math Problem Statement

The annual amounts of rainfall in a certain region are modeled using the normal distribution shown below. The mean of the distribution is 36.04 cm and the standard deviation is 4.9 cm. To proceed, we will use the empirical rule (68-95-99.7 rule), which can help identify the percentage of the total area under the curve within one, two, and three standard deviations of the mean. From the graph, it seems like you need to identify the areas under the curve within certain values (U and V) along the axis. These areas represent the percentages of values within certain ranges of the standard deviation from the mean.

Solution

This is a question involving a normal distribution curve, where the mean is 36.04 cm and the standard deviation is 4.9 cm. To proceed, we will use the empirical rule (68-95-99.7 rule), which can help identify the percentage of the total area under the curve within one, two, and three standard deviations of the mean.

From the graph, it seems like you need to identify the areas under the curve within certain values (U and V) along the axis. These areas represent the percentages of values within certain ranges of the standard deviation from the mean.

Here are the steps to follow:

  1. Identify U and V: Based on the position of U and V along the axis, figure out how many standard deviations they are away from the mean.

    • For example, if U is positioned 1 standard deviation to the left of the mean, then U is at 36.04 - 4.9 = 31.14 cm.
    • Similarly, V could be some other value depending on its placement along the axis.
  2. Apply the empirical rule:

    • 1 standard deviation (68%): This would cover the area from (mean - 1σ) to (mean + 1σ).
    • 2 standard deviations (95%): This would cover the area from (mean - 2σ) to (mean + 2σ).
    • 3 standard deviations (99.7%): This would cover the area from (mean - 3σ) to (mean + 3σ).

Would you like to continue with these calculations based on specific values of U and V? Or do you need further clarification?

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Normal Distribution
Empirical Rule
Standard Deviation
Mean

Formulas

Empirical Rule: 68-95-99.7 rule

Theorems

Empirical Rule (68-95-99.7)

Suitable Grade Level

Grades 9-12