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.
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The range of possible costs for the coal can be determined by taking the margin of error into account.
The margin of error is 3% of the predicted cost, which is $53.00.
3% of $53.00 is (3/100) * $53.00 = $1.59.
Therefore, the range of possible costs for the coal is $53.00 + $1.59 = $54.59 (upper limit) to $53.00 - $1.59 = $51.41 (lower limit).
In other words, the possible costs for the coal can range from $51.41 to $54.59 per ton.
To calculate the range of possible costs for the coal, we need to consider the margin of error.
The margin of error is given as 3%, which means that the actual cost of the coal could be 3% higher or lower than the predicted cost.
To find the range, we can calculate the upper and lower bounds by adding and subtracting the margin of error from the predicted cost.
Upper bound = predicted cost + (margin of error * predicted cost)
= $53.00 + (0.03 * $53.00)
= $53.00 + $1.59
= $54.59
Lower bound = predicted cost - (margin of error * predicted cost)
= $53.00 - (0.03 * $53.00)
= $53.00 - $1.59
= $51.41
Therefore, the range of possible costs for the coal is $51.41 to $54.59 per ton.
To calculate the range of possible costs for the coal, we need to determine the upper and lower limits based on the predicted price and the margin of error.
The margin of error represents the amount by which the predicted price can deviate from the actual price. In this case, the margin of error is 3%.
To calculate the upper limit, we add the margin of error to the predicted price:
Upper limit = Predicted price + (Predicted price * Margin of error)
= $53.00 + ($53.00 * 0.03)
= $53.00 + $1.59
= $54.59
To calculate the lower limit, we subtract the margin of error from the predicted price:
Lower limit = Predicted price - (Predicted price * Margin of error)
= $53.00 - ($53.00 * 0.03)
= $53.00 - $1.59
= $51.41
Therefore, the range of possible costs for the coal is between $51.41 and $54.59 per ton.