Lesson 5

Explore

 

In the Discover section you used an applet to visualize the z-scores and the corresponding area under the normal distribution for OJ Juice Company’s 500-mL bottles of orange juice. In the applet the calculations for the z-scores were shown but the area under the normal curve was just given to you.

 

The area under the normal distribution can be determined either using a z-score table or using a graphing calculator. In Lesson 4 you used the statistics function for normal distribution on your calculator to determine the area under a normal curve to the left of a z-score. The process for determining the area between two z-scores is similar.

 

 

For example, to determine the fraction of bottles that will have a volume between 498.0 mL and 502.0 mL, you need to enter the following into the statistics function for normal distributions on your calculator:

• lower bound
• upper bound
• mean
• standard deviation

 

The area under the normal distribution between 498.0 mL and 502.0 mL is about 0.9923 or 99.23%. Therefore, 99.23% of the bottles of orange juice would have volumes between 498.0 mL and 502.0 mL and would meet the initial quality standard.

 

Another strategy for determining the area under a normal distribution is to use a z-score table.

 

Try This 2

 

Use the interactive applet New Quality Standard to use a z-score table to determine what percentage of bottles will meet the OJ Juice Company’s new quality standard (i.e., a volume between 499.0 mL and 500.5 mL).

 

 

There are different strategies that can be used to determine the area under a normal distribution. Depending on the question or situation, you may find that one strategy is more efficient than the other, or you may find that you are more comfortable using one strategy over another.