Lesson 6
1. Lesson 6
1.3. Explore 2
Module 4: Statistical Reasoning
Self-Check 1
Complete “Practising” questions 5 and 6 on page 303 of your textbook. Note: You will need some of the data that is in question 1 on page 302 in order to complete question 5. Answer
How do confidence intervals, confidence levels, and margins of error relate to the normal distribution?
In Lesson 3 you learned that you can determine the percentage of data that falls between any two whole number standard deviations on the normal curve using the rule of 68-95-99.7. That is, 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations of the mean, and 99.7% of data falls within three standard deviations of the mean.
To interpret this differently, there is a 68% confidence level that a piece of data lies within one standard deviation of the mean, there is a 95% confidence level that a piece of data lies within two standard deviations of the mean, and so on.
The animation titled Normal Curve will help you understand the connection between confidence intervals and the normal curve.
Consider the OJ Juice Company example from Lesson 5. One of the company’s best sellers is a 500-mL bottle of orange juice. When the production process is running smoothly, the volume of juice in the bottles is normally distributed with a mean of 500 mL.
Try This 3
Use the interactive applet titled Check on Quality Standard to determine a 95% confidence interval.
