Q. 1.3 - The Practice of Statistics for AP

Question

The length of human pregnancies from conception to birth varies according to a distribution that is approximately Normal with mean $266$days and standard deviation $16$days.

 Compute the standard deviation of the sampling distribution of$\overline{x}$. Check that the $10\%$ condition is met.

Step-by-Step Solution

Answer

 The standard deviation is $6.532$.

Step1: Given Information

Population mean $\left(\mu \right)=266$

Population standard deviation $\left(\sigma \right)=16$

Sample size $\left(n\right)=6$

Step2: Explanation

The formula to compute the standard deviation is:

${\sigma }_{\overline{x}}=\frac{\sigma }{\sqrt{n}}$

The standard deviation can be calculated as

$$\begin{gathered} {\sigma }_{\overline{x}}=\frac{\sigma }{\sqrt{n}} \\ =\frac{16}{\sqrt{6}} \\ =6.532 \end{gathered}$$