A company sells model cars, trucks, planes, and boats. Before shipping 18,000 of each product a sample of each is tested. Predict how many of each model are defective given the following results.
of 750 cars, 25 are flawed_________________
of 800 trucks, 4 are flawed_______________
of 900 boats, 6 are flawed________________
of 360 planes, 5 are flawed______________
cars : (25/750)(18000) or 600 would be flawed
etc.
S84858
To predict the number of defective models for each category, we can use the concept of proportions. We'll calculate the proportion of defective models based on the tested samples and then apply the proportion to the total number of models.
1. Cars:
Proportion of flawed cars = Number of flawed cars / Total number of tested cars
Proportion of flawed cars = 25 / 750
Proportion of flawed cars = 0.033
Number of defective cars = Proportion of flawed cars * Total number of cars to be shipped
Number of defective cars = 0.033 * 18,000
Number of defective cars = 594
Therefore, it is predicted that 594 model cars will be defective.
2. Trucks:
Proportion of flawed trucks = Number of flawed trucks / Total number of tested trucks
Proportion of flawed trucks = 4 / 800
Proportion of flawed trucks = 0.005
Number of defective trucks = Proportion of flawed trucks * Total number of trucks to be shipped
Number of defective trucks = 0.005 * 18,000
Number of defective trucks = 90
Therefore, it is predicted that 90 model trucks will be defective.
3. Boats:
Proportion of flawed boats = Number of flawed boats / Total number of tested boats
Proportion of flawed boats = 6 / 900
Proportion of flawed boats = 0.0067
Number of defective boats = Proportion of flawed boats * Total number of boats to be shipped
Number of defective boats = 0.0067 * 18,000
Number of defective boats = 120.6 (rounding to 121)
Therefore, it is predicted that 121 model boats will be defective.
4. Planes:
Proportion of flawed planes = Number of flawed planes / Total number of tested planes
Proportion of flawed planes = 5 / 360
Proportion of flawed planes = 0.0139
Number of defective planes = Proportion of flawed planes * Total number of planes to be shipped
Number of defective planes = 0.0139 * 18,000
Number of defective planes = 250.2 (rounding to 250)
Therefore, it is predicted that 250 model planes will be defective.
In summary:
- The predicted number of defective model cars is 594.
- The predicted number of defective model trucks is 90.
- The predicted number of defective model boats is 121.
- The predicted number of defective model planes is 250.
To predict the number of defective models, we need to calculate the ratio of flawed models in the sample and then apply that ratio to the total number of each model.
First, let's calculate the ratio of flawed models for each type:
For cars:
Ratio of flawed cars = (Number of flawed cars) / (Total number of cars in the sample)
Ratio of flawed cars = 25 / 750 = 1/30
Now, let's apply this ratio to the total number of cars:
Total number of cars = 18,000
Number of defective cars = Total number of cars * Ratio of flawed cars
Number of defective cars = 18,000 * (1/30)
Number of defective cars = 600
Similarly, for trucks:
Ratio of flawed trucks = (Number of flawed trucks) / (Total number of trucks in the sample)
Ratio of flawed trucks = 4 / 800 = 1/200
Total number of trucks = 18,000
Number of defective trucks = Total number of trucks * Ratio of flawed trucks
Number of defective trucks = 18,000 * (1/200)
Number of defective trucks = 90
For boats:
Ratio of flawed boats = (Number of flawed boats) / (Total number of boats in the sample)
Ratio of flawed boats = 6 / 900 = 1/150
Total number of boats = 18,000
Number of defective boats = Total number of boats * Ratio of flawed boats
Number of defective boats = 18,000 * (1/150)
Number of defective boats = 120
For planes:
Ratio of flawed planes = (Number of flawed planes) / (Total number of planes in the sample)
Ratio of flawed planes = 5 / 360 = 1/72
Total number of planes = 18,000
Number of defective planes = Total number of planes * Ratio of flawed planes
Number of defective planes = 18,000 * (1/72)
Number of defective planes = 250
Therefore, the predicted number of defective models is as follows:
- Defective cars: 600
- Defective trucks: 90
- Defective boats: 120
- Defective planes: 250