In 2017, the entire fleet of light-duty vehicles sold in the United States by each manufacturer must emit an average of no more than 84 milligrams per mile (mg/mi) of nitrogen oxides (NOX) and nonmethane organic gas (NMOG) over the useful life (150,000 miles of driving) of the vehicle. NOX + NMOG emissions over the useful life for one car model vary Normally with mean 78 mg/mi and standard deviation 6 mg/mi. (a) What is the probability that a single car of this model emits more than 84 mg/mi of NOX+ NMOG? (Enter your answer rounded to four decimal places.) probability: mbability that the average NOX+ NMOG level i of
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
![### Emissions Standards for Light-Duty Vehicles
In 2017, regulations required that the fleet of light-duty vehicles sold in the United States by each manufacturer must, on average, emit no more than 84 milligrams per mile (mg/mi) of nitrogen oxides (NOX) and nonmethane organic gases (NMOG) over the vehicle's useful life of 150,000 miles. The emissions of NOX + NMOG over this period for a single car model follow a normal distribution with a mean of 78 mg/mi and a standard deviation of 6 mg/mi.
#### Problem (a)
**Question:** What is the probability that a single car of this model emits more than 84 mg/mi of NOX + NMOG? (Please enter your answer rounded to four decimal places.)
**Probability:** [Input field]
#### Problem (b)
**Scenario:** A company has 36 cars of this model in its fleet. What is the probability that the average NOX + NMOG level exceeds 84 mg/mi?
(Note: The details for part (b) are incomplete in the image.)
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Ensure you utilize a standard normal distribution table or appropriate statistical software to find these probabilities. Consider the Central Limit Theorem for part (b), as it involves a sample distribution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2fb7a5f7-d1fe-47c3-ab51-c010c8f81dff%2F9c6e95fb-753d-4a7f-83e2-b2d23b06c0f6%2Fiwe0g7e_processed.jpeg&w=3840&q=75)
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