Question

The size of fish is very important to commercial fishing. A study conducted in 2012 found the length of Atlantic cod caught in nets in Karlskrona to have a mean of 47.8 cm and a standard deviation of 3.72 cm (Ovegard, Berndt & Lunneryd, 2012). Assume the length of fish is normally distributed. What is the length in cm of the longest 10% of Atlantic cod in this area? Round answer to 2 decimal places. Answer:

Answer 1

Solution :

Given that,  

mean = = 47.8

standard deviation = = 3.72

Using standard normal table ,

P(Z > z) = 10%

1 - P(Z < z) = 0.1

P(Z < z) = 1 - 0.1

P(Z < 1.28) = 0.9

z = 1.28

Using z-score formula,

x = z * +

x = 1.28 * 3.72 + 47.8 = 52.56

The length in cm of the longest 10% of Atlantic cod in this area 52.56 cm