A factory produces cereal bars with mass 58 g, and percentage error up to 2%. Find the interval of possible masses of cereal bars from this factory.
To find the interval of possible masses, we need to consider the maximum and minimum values that the mass could be, given the percentage error.
The maximum mass will be the original mass plus the maximum percentage error:
Maximum mass = 58 g + (2% of 58 g) = 58 g + (0.02)(58 g) = 58 g + 1.16 g = 59.16 g
The minimum mass will be the original mass minus the maximum percentage error:
Minimum mass = 58 g - (2% of 58 g) = 58 g - (0.02)(58 g) = 58 g - 1.16 g = 56.84 g
Therefore, the interval of possible masses of cereal bars from this factory is from 56.84 g to 59.16 g.
To find the interval of possible masses of cereal bars from this factory, we need to consider the percentage error.
1. Calculate the maximum allowable error based on the given percentage error:
Maximum Allowable Error = (Percentage Error / 100) * Mass of the cereal bar
Given:
Percentage Error = 2%
Mass of the cereal bar = 58 g
Maximum Allowable Error = (2 / 100) * 58
= 0.02 * 58
= 1.16 g
2. Determine the lower limit of the interval by subtracting the maximum allowable error from the mass of the cereal bar:
Lower Limit = Mass of the cereal bar - Maximum Allowable Error
= 58 - 1.16
= 56.84 g
3. Determine the upper limit of the interval by adding the maximum allowable error to the mass of the cereal bar:
Upper Limit = Mass of the cereal bar + Maximum Allowable Error
= 58 + 1.16
= 59.16 g
Therefore, the interval of possible masses of cereal bars from this factory is [56.84 g, 59.16 g].
To find the interval of possible masses of the cereal bars, we need to consider the percentage error.
Percentage error is calculated by taking the absolute difference between the measured value and the true value, dividing it by the true value, and then multiplying by 100.
In this case, the true mass of the cereal bar is 58 g, and the percentage error is up to 2%.
To calculate the maximum possible mass, we use the formula:
Maximum possible mass = true mass + (percentage error * true mass)
= 58 g + (2% * 58 g)
= 58 g + (0.02 * 58 g)
= 58 g + 1.16 g
= 59.16 g
To calculate the minimum possible mass, we use the formula:
Minimum possible mass = true mass - (percentage error * true mass)
= 58 g - (2% * 58 g)
= 58 g - (0.02 * 58 g)
= 58 g - 1.16 g
= 56.84 g
Therefore, the interval of possible masses of the cereal bars from this factory is 56.84 g to 59.16 g.