Lesson 5
1. Lesson 5
1.3. Explore 2
Self-Check 1
In an effort to have more bottles meet the new quality standard of volumes between 499.0 mL and 500.5 mL, OJ Juice Company made changes to its equipment and production process. When data was collected on the new production process, the volume of juice in the bottles was normally distributed with a mean of 500 mL and a standard deviation of 0.45 mL.
If the production process produces 15 000 bottles in one day, determine how many of these bottles will now meet the quality standard of a volume between 499.0 mL and 500.5 mL.
Read “Example 4: Solving a quality control problem” on pages 288 to 290 of your textbook. As you read over Logan’s and Nathan’s solutions, consider the effect of using rounded values from a z-score table versus using the complete values for the statistical function on a graphing calculator. Which gives the more accurate answer?
Self-Check 2
Complete “Practising” question 11 on page 292 of your textbook. Answer
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In Lesson 4 you learned how normal distributions help manufacturers determine the fraction of their products that last over a certain period of time. Normal distributions can also be used to help manufacturers determine what length of warranty to offer.
Try This 3
Recall the Millennium Mufflers from Lesson 4. The lifetime of the best-selling muffler, the Millennium Muffler, is normally distributed with a mean of 7.2 years and a standard deviation of 1.8 years. Suppose the muffler company wanted to determine what length of warranty to offer to restrict the number of muffler claims to less than 5% of the Millennium Mufflers sold. View the animation Length of Warranty for a Millennium Muffler.
muffler: iStockphoto/Thinkstock