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

Answer:

Step-by-step 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 $P(X>\mu+x)=0.01$

$\Rightarrow P(\frac{X-\mu}{0.8}>\frac{x}{0.8})=0.01 \\\\\Rightarrow P(\frac{X-\mu}{0.8}\leq \frac{x}{0.8})=0.99 \\\\\Rightarrow \Phi(\frac{x}{0.8})=0.99 \\\\\Rightarrow \frac{x}{0.8}=\Phi^{-1}(0.99)=2.32635 \\\\\Rightarrow x=2.32635*0.8=1.86108$