An investor predicts that next month, 1 ton of coal will cost $53.00, with a 3% margin of error. Based on the prediction, what is the range of possible costs, in dollars per ton, for the coal? Explain your answer.
To calculate the range of possible costs for the coal, we need to consider the 3% margin of error.
The margin of error is the amount by which the predicted value can vary. We can find the margin of error by multiplying the predicted value by the margin of error percentage:
Margin of Error = Predicted Value * Margin of Error Percentage
For a 3% margin of error, the margin of error percentage is 3/100 = 0.03.
Margin of Error = $53.00 * 0.03 = $1.59
Now, we can find the range of possible costs by adding and subtracting the margin of error from the predicted value:
Range of Possible Costs = Predicted Value ± Margin of Error
Lower Range = $53.00 - $1.59 = $51.41
Upper Range = $53.00 + $1.59 = $54.59
Therefore, the range of possible costs for the coal is $51.41 to $54.59 per ton.
This means that there is a 97% (100% - 3%) chance the cost of the coal will fall within this range.
To determine the range of possible costs for the coal, we need to take into account the margin of error.
The margin of error is given as 3% of the predicted cost.
To calculate the margin of error, we can multiply the predicted cost by the margin of error percentage:
Margin of Error = 3% of $53.00
= (3/100) * $53.00
= $1.59
To find the range of possible costs, we add and subtract the margin of error to the predicted cost:
Lower Range = Predicted Cost - Margin of Error
= $53.00 - $1.59
= $51.41
Upper Range = Predicted Cost + Margin of Error
= $53.00 + $1.59
= $54.59
Therefore, based on the prediction and given margin of error, the range of possible costs for the coal is between $51.41 and $54.59 per ton.
To determine the range of possible costs for the coal, we can use the margin of error provided. The margin of error is given as 3% of the predicted cost, which is $53.00.
To find the margin of error, we can calculate 3% of $53.00.
Step 1: Convert 3% to a decimal by dividing it by 100: 3/100 = 0.03.
Step 2: Multiply the decimal by the predicted cost to find the margin of error: 0.03 * $53.00 = $1.59.
So, the margin of error is $1.59.
The range of possible costs can be determined by adding and subtracting the margin of error from the predicted cost.
The highest possible cost is obtained by adding the margin of error to the predicted cost: $53.00 + $1.59 = $54.59.
The lowest possible cost is obtained by subtracting the margin of error from the predicted cost: $53.00 - $1.59 = $51.41.
Therefore, the range of possible costs for the coal next month is between $51.41 and $54.59 per ton.