https://file.aiquickdraw.com/mathbot/file/1725657346095tnb9sj1c.jpg

The problem in the image asks to calculate tolerance intervals based on a normal distribution. Specifically, you're given three probabilities:

1. **68.26%**
2. **95.44%**
3. **99.73%**

These percentages refer to the areas under the normal curve within a certain number of standard deviations from the mean, which correspond to:

1. **68.26%** ≈ within **1 standard deviation** of the mean (\( z = 1 \))
2. **95.44%** ≈ within **2 standard deviations** of the mean (\( z = 2 \))
3. **99.73%** ≈ within **3 standard deviations** of the mean (\( z = 3 \))

Now, let's proceed with the calculations.

The tolerance intervals for a normal distribution are determined as:
\[
 \text{Interval} = \mu \pm z \cdot \sigma
\]
Where:
- \( \mu \) is the mean of the distribution
- \( z \) is the z-score (which you need to find based on the given percentages)
- \( \sigma \) is the standard deviation

To compute the intervals, I will round the z-scores and results to two decimal places as instructed.

Let me know if you want to proceed with an example or any clarifications. Would you like to provide the mean (\( \mu \)) and standard deviation (\( \sigma \)) so I can calculate the intervals?

Assuming that the distribution of entertainment expenses is approximately normally distributed, calculate estimates of tolerance intervals containing 68.26 percent, 95.44 percent, and 99.73 percent of all entertainment expenses by the sales force. Round intermediate calculations and final answers to 2 decimals.

Learn how to calculate tolerance intervals for a normal distribution, covering 68.26%, 95.44%, and 99.73% of data. This example uses the 68-95-99.7 rule and includes a detailed explanation of the process, suitable for undergraduate statistics students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation