High School

Thank you for visiting Given the data has a bell shaped distribution with a mean of 35 9 and a standard deviation of 9 6 1 Find the 68. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!

Given the data has a bell-shaped distribution with a mean of 35.9 and a standard deviation of 9.6:

1. Find the 68% interval according to the empirical rule.
2. Find the usual range according to the empirical rule.

Answer :

To address the student's question, we need to use the empirical rule, which applies to bell-shaped (normal) distributions. The empirical rule states:

  1. Approximately 68% of data falls within one standard deviation of the mean.
  2. Approximately 95% falls within two standard deviations.
  3. Approximately 99.7% falls within three standard deviations.

Given that the mean [tex]\mu[/tex] is 35.9 and the standard deviation [tex]\sigma[/tex] is 9.6, let's find the 68% interval:

First, calculate the interval for one standard deviation from the mean:

  • Lower bound: [tex]\mu - \sigma = 35.9 - 9.6 = 26.3[/tex]
  • Upper bound: [tex]\mu + \sigma = 35.9 + 9.6 = 45.5[/tex]

So, the 68% interval is between 26.3 and 45.5.

Next, for the usual range:

According to the empirical rule (or the typical definition of the usual range), it's often interpreted as the range in which 95% of data falls.

  • Lower bound: [tex]\mu - 2\sigma = 35.9 - 2(9.6) = 35.9 - 19.2 = 16.7[/tex]
  • Upper bound: [tex]\mu + 2\sigma = 35.9 + 2(9.6) = 35.9 + 19.2 = 55.1[/tex]

Therefore, the usual range is between 16.7 and 55.1.

In conclusion:

  • 68% interval: From 26.3 to 45.5
  • Usual range (95% of data): From 16.7 to 55.1

Thank you for reading the article Given the data has a bell shaped distribution with a mean of 35 9 and a standard deviation of 9 6 1 Find the 68. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!

Rewritten by : Jeany

Other Questions