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

Solution:

Given:

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

Using the Z-score formula;

$\begin{gathered} Z=\frac{x-\mu}{\sigma} \\ Z=\frac{0.27-0.2}{0.05} \\ Z=\frac{0.07}{0.05} \\ Z=1.4 \end{gathered}$

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