SOLUTION: The distribution of the weights of a sample of 1,400 cargo containers is symmetric and bell-shaped According to the Empirical Rule, what percent of the weights will lie between

Question 1191332: The distribution of the weights of a sample of 1,400 cargo containers is symmetric and bell-shaped
According to the Empirical Rule, what percent of the weights will lie between X⎯⎯⎯−2s and X⎯⎯⎯+2s ?

According to the Empirical Rule, what percent of the weights will lie between X⎯⎯⎯ and X⎯⎯⎯+2s ?

According to the Empirical Rule, what percent of the weights will lie below X⎯⎯⎯−2s ?

i need to see steps
Answer by CPhill(1959) (Show Source): You can put this solution on YOUR website!
Here's how the Empirical Rule applies to this situation:
* **Empirical Rule:** The Empirical Rule (also known as the 68-95-99.7 Rule) applies to distributions that are symmetric and bell-shaped (approximately normal). It states that:
* Approximately 68% of the data falls within 1 standard deviation of the mean (between X̄ - s and X̄ + s).
* Approximately 95% of the data falls within 2 standard deviations of the mean (between X̄ - 2s and X̄ + 2s).
* Approximately 99.7% of the data falls within 3 standard deviations of the mean (between X̄ - 3s and X̄ + 3s).
* **Between X̄ - 2s and X̄ + 2s:** According to the Empirical Rule, approximately **95%** of the weights will lie between X̄ - 2s and X̄ + 2s.
* **Between X̄ and X̄ + 2s:** Since the distribution is symmetric, half of the 95% will lie between the mean and 2 standard deviations above the mean. Therefore, approximately 95%/2 = **47.5%** of the weights will lie between X̄ and X̄ + 2s.
* **Below X̄ - 2s:** Since 95% of the data is between X̄ - 2s and X̄ + 2s, the remaining 5% is outside this range. Because the distribution is symmetric, half of this 5% (2.5%) will be below X̄ - 2s, and the other half (2.5%) will be above X̄ + 2s. Therefore, approximately **2.5%** of the weights will lie below X̄ - 2s.

RELATED QUESTIONS
The distribution of weights of a sample of 1400 cargo containers is symmetric and bell... (answered by Boreal)

What is the distribution of the weights of a sample of 1,300 cargo containers is... (answered by Solver92311)

The distribution of the weights of a sample of 1,375 cargo containers is symmetric and... (answered by Boreal)

The distribution of weights of a sample of 1,400 is symmetric and bell-shaped. According... (answered by stanbon)

2.Which of the following is NOT a characteristic of the normal distribution? Answer... (answered by richard1234)

1. Which of the following statements are correct? a. A normal distribution is any... (answered by stanbon)

The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. (answered by Theo)

Which of the following statements are correct? a. A normal distribution is any... (answered by neatmath)

Which of the following statements are correct? a. A normal distribution is any... (answered by edjones)