Question

13#Suppose that the antenna lengths of woodlice are approximately normally distributed with a mean of 0.2 inches and a standard deviation of 0.05 inches. What proportion of woodlice have antenna lengths that are at least 0.27 inches? Round your answer to at least four decimal places.

Answer 1

Given:

`\begin{gathered} \mu=0.2 \\ \sigma=0.05 \\ x=0.27 \end{gathered}`

Using the Z-score formula;

`\begin{gathered} Z=(x-\mu)/(\sigma) \\ Z=(0.27-0.2)/(0.05) \\ Z=(0.07)/(0.05) \\ Z=1.4 \end{gathered}`

From the Z-scores table;

`\begin{gathered} P(x\ge Z)=0.080757 \\ \\ \\ To\text{ four decimal places;} \\ P(x\ge Z)=0.0808 \end{gathered}`

Therefore, the proportion of woodlice have antenna lengths that are at least 0.27 inches is 0.0808