Final Answer:
The probability that a randomly chosen truck would generate between 0.65 grams per mile and 2.25 grams per mile of NOX gases is approximately 0.6826 or 68.26%.
Step-by-step explanation:
The given problem involves a normal distribution of NOX levels in the exhaust of a light truck model, with a specified mean and standard deviation.
To find the probability that a randomly chosen truck falls within a certain range of NOX levels, we can use the properties of the normal distribution.
The mean (μ) is given as -1.45 grams per mile, and the standard deviation (σ) is given as 0.40 grams per mile. These parameters define the normal distribution curve.
The probability between two values, in this case, 0.65 grams per mile and 2.25 grams per mile, can be found by standardizing these values and using the Z-score formula.
First, we calculate the Z-scores for the lower and upper limits using the formula Z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.
Once we have the Z-scores, we can use a standard normal distribution table or a calculator to find the corresponding probabilities.
In this case, the probability is the area under the curve between the Z-scores for 0.65 and 2.25. The result is the probability that a randomly chosen truck would generate NOX gases within this specified range, which is approximately 0.6826 or 68.26%.
This is a common interpretation in statistics, where the range represents a certain percentage of the total distribution.