The Park Protectors is a group of elementary students and teachers from 32 schools who pick up trash at local parks. The line pl
ot shows the tons of trash they picked up this year.
There are 32 schools in the group. How much trash did each school pick up this year?
Each school picked up
tons of trash equally.
You may use the scratchpad to show your work.
There are 32 schools in the group. How much trash did each school pick up this year?
Each school picked up
tons of trash equally.
You may use the scratchpad to show your work.
2 answers:
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Answer:
The level is L = 0.084
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution:
Problems of normally distributed samples can be 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 normally distributed random variable X, with mean and standard deviation
, the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
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 is L = 0.084