Question

Garden delicious pea pods have lengths that are approximately normally distributed with standard deviation 0.8 inches. the largest 1 percent of pods are eligible for prizes. how many inches above the mean pod length is the smallest pod that is eligible for a prize?

Answer 1

Explanation:

Let X denotes the length of a randomly selected garden delicious pea pod.

`X\sim Normal(\mu,0.8^2)`

To find x such that
`P(X>\mu+x)=0.01`

`\Rightarrow P((X-\mu)/(0.8)>(x)/(0.8))=0.01 \\\\\Rightarrow P((X-\mu)/(0.8)\leq (x)/(0.8))=0.99 \\\\\Rightarrow \Phi((x)/(0.8))=0.99 \\\\\Rightarrow (x)/(0.8)=\Phi^(-1)(0.99)=2.32635 \\\\\Rightarrow x=2.32635*0.8=1.86108`