Answer:
The length of the longest 15% of Atlantic cod in this area is 53.79cm, roundeed to 2 decimal places.
Step-by-step explanation:
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
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.
In this problem, we have that:
A study conducted in 2012 found the length of Atlantic cod caught in nets in Karlskrona to have a mean of 49.9 cm and a standard deviation of 3.74 cm, so .
What is the length in cm of the longest 15% of Atlantic cod in this area?
We have to find the value of X for the value of Z that has a pvalue of 0.85.
Looking at the zscore table, we have that Z = 1.04 has a pvalue of 0.8508. So, we have to find the value of X when .
So
The length of the longest 15% of Atlantic cod in this area is 53.79cm, roundeed to 2 decimal places.