Answer:
The level L such that the probability that the average NOX level x for the fleet is greater than L is only 0.01 is L = 0.065.
Explanation:
To solve this question, we have to understand the normal probability distribution and the central limit theorem:
Normal probability distribution:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean
and standard deviation
, the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit theorem:
The Central Limit Theorem estabilishes that, for a random variable X, with mean
and standard deviation
, a large sample size can be approximated to a normal distribution with mean
and standard deviation, which is also called standard error

In this problem, we have that:

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?
This is X when Z has a pvalue of 1-0.01 = 0.99. So it is X when Z = 2.325.

By the Central Limit Theorem




The level L such that the probability that the average NOX level x for the fleet is greater than L is only 0.01 is L = 0.065.