The level of nitrogen oxides (nox) in the exhaust after 50,000 miles or fewer of driving of cars of a particular model varies normally with mean 0.03 g/mi and standard deviation 0.01 g/mi. a company has 64 cars of this model in its fleet. what is the level l such that the probability that the average nox level x for the fleet is greater than l is only 0.01? (hint: this requires a backward normal calculation. round your answer to three decimal places.)
Accepted Solution
A:
Answer: 0.533
Explanation: Note that
[tex]x \ \textgreater \ I \\ \Leftrightarrow x - 0.3 \ \textgreater \ I - 0.3 \\ \\ \Leftrightarrow \boxed{\frac{x - 0.3}{0.1} \ \textgreater \ \frac{I - 0.3}{0.1}} (1) [/tex]
Let
[tex]z_1[/tex] = z-score for I. [tex]z_2[/tex] = z-score for x.
Since [tex]z_1[/tex] and [tex]z_2[/tex] are z-scores and the level of nitrogen oxides are normally distributed, using normal distribution calculator (or table),