Chapter 8, Problem 40RE

To determine

To find : the proportion of $3$ year old yellow perch raised under similar condition can be expected to reach a length of $20$ cm or more.

Answer to Problem 40RE

At $20.51\%$ to reach a length of $20$ cm or more.

Explanation of Solution

Given information : A researcher measures the length of $3$ year old yellow perch in a fish hatchery and they have a mean length of $17.2$ cm with a standard deviation of $3.4$ cm.

Calculation :

Assuming normality of the height:

  $\begin{array}{l}P\left(x\ge 20\right)=1-P\left(\frac{x-17.2}{3.4}\le \frac{20-17.2}{3.4}\right)\\ \Rightarrow 1-\varphi \left(0.8235\right)\\ \Rightarrow 0.2051\\ \Rightarrow 20.51\%\end{array}$