REI- What’s Your Tolerance
Alignments to standards:
Manufacturing Tolerances III
The bottle industry tries to fill each bottle to the maximum amount of volume listed on the bottle. Some bottles are overfilled and some are under-filled. This error is called tolerance.
- Ø Bottle Us has a 0.3 ounce tolerance for a bottle of pop advertised to be 27 ounces.
- Write an absolute value inequality to represent the possible volumes of the pop bottle.
- Define your variable(s).
- Solve the inequality and write your solution as a compound inequality.
Bottle Us also manufactures cans of juice and energy drinks.
- Ø The function f(x) = represents the tolerance, for a can of juice with volume x. The function represents the tolerance for a can of energy drink with volume x.
- Graph the function
- Graph the function
- Please use graph paper
- Ø Describe two ways that the graph of g(x) differs from the graph of f(x).
- Ø The quality manager of the pop company has determined that production is successful is no more than 25% of the pop bottles are outside of the allowed tolerance interval.
- Use the box-and-whisker plot below to determine if the company is meeting this standard.
- Justify your answer.
- Ø The CEO of the same pop company has determined that tolerance intervals on bottle production must be tightened up. The CEO issued a memo to the production manager that new pop bottle production will be successful if no more than 16% of the pop bottles are outside of the allowed tolerance interval.
- Can you use the box-and-whisker plot above to determine if the company is currently meeting the new standard?
- Justify your answer.
Manufacturing Tolerances III (Answer Key)
The bottle industry tries to fill each bottle to the maximum amount of volume listed on the bottle. Some bottles are overfilled and some are under-filled. This error is called tolerance.
- Ø Bottle Us has a 0.3 ounce tolerance for a bottle of pop advertised to be 27 ounces.
- Write an absolute value inequality to represent the possible volumes of the pop bottle.
- Define your variable(s).
- Solve the inequality and write your solution as a compound inequality.
|x-27|>0.3
x is the possible volumes of the soda bottle
|x-27|>-0.3 and |x-27|<0.3
add 27 to both sides
x>26.7 x<27.3
Bottle Us also manufactures cans of juice and energy drinks.
- Ø The function f(x) = represents the tolerance, for a can of juice with volume x. The function represents the tolerance for a can of energy drink with volume x.
- Graph the function
- Graph the function
- Please use graph paper
- Ø Describe two ways that the graph of g(x) differs from the graph of f(x).
g(x) has a steep slope, making the graph wider
the two graphs have different vertices
- Ø The quality manager of the pop company has determined that production is successful is no more than 25% of the pop bottles are outside of the allowed tolerance interval.
- Use the box-and-whisker plot below to determine if the company is meeting this standard.
- Justify your answer.
yes, the company is meeting it’s standard because there is less than 25% left outside of the interval since 27.3 is the upper extreme, and 26.7 lies within the lower quartile.
- Ø The CEO of the same pop company has determined that tolerance intervals on bottle production must be tightened up. The CEO issued a memo to the production manager that new pop bottle production will be successful if no more than 16% of the pop bottles are outside of the allowed tolerance interval.
- Can you use the box-and-whisker plot above to determine if the company is currently meeting the new standard?
- Justify your answer.
No, you cannot use the box-and-whisker plot to determine 16% because you can only guarantee increments of 25%.
The link to the lesson with graphs, and answers is posted below: