Question

Alaskan Salmon are fished extensively to serve in restaurants. However, there are limits to how many and the size of fish which are allowed to be kept. Generally, fishermen are not allowed to keep smaller, younger fish. If salmon size is normally distributed and the average salmon taken from Alaskan waters is 12.5 inches with a standard deviation of 3.3, what length of salmon would represent the bottom 25% of all salmon?

Answer 1

The salmon size is less than equal to 10.28 inches represent bottom 25% of all salmon.

Explanation:

We are given the following information in the question:

Mean, μ = 12.5 inches

Standard Deviation, σ = 3.3

We are given that the distribution of salmon size is a bell shaped distribution that is a normal distribution.

Formula:

`z_(score) = \displaystyle(x-\mu)/(\sigma)`

We have to find the value of x such that the probability is 0.25

`P( X < x) = P( z < \displaystyle(x - 12.5)/(3.3))=0.25`

Calculation the value from standard normal z table, we have,

`\displaystyle(x - 12.5)/(3.3) = -0.674\\\\x = 10.2758\approx 10.28`

Thus, the salmon size is equal to or less than 10.28 inches, they are considered small and young and represent bottom 25% of all salmon.