https://file.aiquickdraw.com/mathbot/file/1726580932786oqzvr0zh.jpg

Let's break down the problem based on the image you provided:

The Acme Company manufactures widgets with weights that are normally distributed. 
- Mean (µ) = 44 ounces
- Standard deviation (σ) = 7 ounces

We will use the **Empirical Rule** (also known as the 68-95-99.7 rule) to answer the questions.

### a) 95% of the widget weights lie between:

According to the Empirical Rule:
- 95% of data falls within **2 standard deviations** of the mean.
  
Thus, the weights would lie between:
\[
\mu - 2\sigma \quad \text{and} \quad \mu + 2\sigma
\]

Calculating these values:
\[
44 - 2(7) = 44 - 14 = 30
\]
\[
44 + 2(7) = 44 + 14 =

The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped with a mean of 44 ounces and a standard deviation of 7 ounces. Using the Empirical Rule, answer the following questions:

a) 95% of the widget weights lie between __ and __.

b) What percentage of the widget weights lie between 23 and 58 ounces?

c) What percentage of the widget weights lie below 51?

Learn how to apply the Empirical Rule to a normal distribution with a mean of 44 ounces and a standard deviation of 7 ounces. Determine the range for 95% of data, calculate the percentage of data between specific values, and find the percentage of weights below a certain threshold. Suitable for high school students studying statistics.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation