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Math  /  Data & Statistics

QuestionProblema 2. En la elaboración de una bebida se desea garantizar que el porcentaje de CO (gas) por envase esté entre 2.5 y 3.0. Los siguientes datos son obtenidos del monitoreo del proceso: 2.612 .622 .652 .562 .682 .512 .562 .622 .632 .572 .602 .532 .692 .53 2.672.662.632.522.612.602.522.622.672.582.612.642.492.582.612.532.672 .662 .63 \quad 2.52 \quad 2.612 .602 .522 .622 .672 .582 .612 .642 .492 .582 .612 .53 2.532.572.662.512.572.552.572.562.522.582.642.592.572.582.522.612.532 .572 .662 .51 \quad 2.572 .552 .572 .562 .522 .582 .642 .592 .572 .582 .522 .61 2.552.552.732.512.612.712.642.592.602.642.562.602.5才2.482.602.612.55 \quad 2.55 \quad 2.732 .51 \quad 2.61 \quad 2.712 .642 .592 .60 \quad 2.642 .562 .602 .5 才 \quad 2.482 .602 .61 2.552 .662 .692 .562 .642 .67 2.73

Studdy Solution

STEP 1

1. The given percentages of CO (gas) in the beverage are recorded for multiple samples.
2. The desired range for the CO percentage per container is between 2.5 and 3.0.
3. The goal is to analyze the provided data to determine if the percentage of CO in the samples stays within the desired range.

STEP 2

1. List all the provided data points.
2. Count how many data points fall within the desired range (2.5 to 3.0).
3. Calculate the percentage of data points that fall within the desired range.
4. Interpret the results to determine the consistency of the CO percentage in the beverage samples.

STEP 3

List all the provided data points.
{2.612,.622,.652,.562,.682,.512,.562,.622,.632,.572,.602,.532,.692,.53,2.672,.662,.63,2.52,2.612,.602,.522,.622,.672,.582,.612,.642,.492,.582,.612,.53,2.532,.572,.662,.51,2.572,.552,.572,.562,.522,.582,.642,.592,.572,.582,.522,.61,2.55,2.55,2.732,.51,2.61,2.712,.642,.592,.60,2.642,.562,.602,.5,2.482,.602,.61,2.552,.662,.692,.562,.642,.67,2.73} \{2.612, .622, .652, .562, .682, .512, .562, .622, .632, .572, .602, .532, .692, .53, 2.672, .662, .63, 2.52, 2.612, .602, .522, .622, .672, .582, .612, .642, .492, .582, .612, .53, 2.532, .572, .662, .51, 2.572, .552, .572, .562, .522, .582, .642, .592, .572, .582, .522, .61, 2.55, 2.55, 2.732, .51, 2.61, 2.712, .642, .592, .60, 2.642, .562, .602, .5, 2.482, .602, .61, 2.552, .662, .692, .562, .642, .67, 2.73 \}

STEP 4

Filter the data points to only include those between 2.5 and 3.0.

STEP 5

Count the number of data points that fall within the range 2.5 to 3.0.
Filtered data points: {2.612,2.672,2.52,2.532,2.572,2.55,2.55,2.732,2.61,2.712,2.642,2.552,2.642,2.73} \{2.612, 2.672, 2.52, 2.532, 2.572, 2.55, 2.55, 2.732, 2.61, 2.712, 2.642, 2.552, 2.642, 2.73\}
Number of data points within the range = 14

STEP 6

Calculate the total number of provided data points.
Total number of data points = 65

STEP 7

Calculate the percentage of data points that fall within the desired range.
Percentage=(1465)×100≈21.54% \text{Percentage} = \left( \frac{14}{65} \right) \times 100 \approx 21.54\%

STEP 8

Interpret the results: Only approximately 21.54% of the samples have CO percentages within the desired range of 2.5 to 3.0.
Solution: The percentage of samples with CO within the desired range is approximately 21.54%.

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